Edit Profile de la Llave, Rafael Compute Distance To: Compute Author ID: de-la-llave.rafael Published as: De La Llave, R.; De La Llave, Rafael; De la Llave, R.; De la Llave, Rafael; De la Lĺave, R.; La Llave, Rafael De; de La Llave, Rafael; de la Llave, R.; de la Llave, Rafael Homepage: http://people.math.gatech.edu/~rll6/ External Links: MGP · Wikidata · ORCID · ResearchGate · dblp Documents Indexed: 162 Publications since 1982, including 5 Books all top 5 Co-Authors 24 single-authored 11 Fontich, Ernest 10 Calleja, Renato C. 10 M-Seara, Tere 9 Delshams, Amadeu 9 Valdinoci, Enrico 7 Celletti, Alessandra 7 Gidea, Marian 7 Su, Xifeng 6 Petrov, Nikola P. 6 Sire, Yannick 5 Haro, Àlex 5 Martín, Pau 4 González-Enríquez, Alejandra 4 Moriyón, Roberto 4 Wayne, C. Eugene 4 Windsor, Alistair 3 Blass, Timothy 3 Cabré, Xavier 3 Falcolini, Corrado 3 Huguet, Gemma 3 Jiang, Miaohua 3 Marco, José Manuel 3 Olvera, Arturo 3 Tompaidis, Stathis 2 Banyaga, Augustin 2 Blazevski, Daniel 2 Caffarelli, Luis Ángel 2 Cheng, Hongyu 2 Díaz-Espinosa, Oliver 2 Fefferman, Charles Louis 2 Figueras, Jordi-Lluís 2 He, Xiaolong 2 Jorba, Àngel 2 Koch, Hans-Friedrich 2 Li, Xuemei 2 Mireles-James, Jason D. 2 Obaya, Rafael 2 Panayotaros, Panayotis 2 Pesin, Yakov Borisovich 2 Radin, Charles 2 Rana, David 1 Adomaitis, Raymond A. 1 Alishah, Hassan Najafi 1 Apte, Amit 1 Baldomá, Immaculada 1 Canadell, Marta 1 Candel, Alberto 1 Capinski, Maciej J. 1 Cordoba, Diego 1 Corsi, Livia 1 Fox, Adam M. 1 Gameiro, Marcio F. 1 González, Oscar R. 1 Haddad, Wassim Michael 1 Itin, A. P. 1 Katok, Anatole B. 1 Kevrekidis, Ioannis George 1 Kogelbauer, Florian 1 Lessard, Jean-Philippe 1 Lomelí, Héctor E. 1 Lorenz, Jens 1 Luque, Alejandro 1 Neishtadt, Anatoly I. 1 Petzold, Linda Ruth 1 Sadovskaya, Victoria 1 Salahshoor, Hossein 1 Shirani, Farshad 1 Shub, Michael 1 Simó, Carles 1 Vano, John A. 1 Vasiliev, Alexei A. 1 Villanueva, Jordi 1 Wang, Fenfen 1 Weiss, Howard 1 Zhang, Lei 1 Zhang, Lei 1 Zhang, Lei 1 Zou, Maorong all top 5 Serials 13 Journal of Statistical Physics 13 Discrete and Continuous Dynamical Systems 11 Journal of Differential Equations 9 Communications in Mathematical Physics 9 Nonlinearity 8 SIAM Journal on Applied Dynamical Systems 7 Ergodic Theory and Dynamical Systems 7 SIAM Journal on Mathematical Analysis 4 Advances in Mathematics 4 Physica D 4 Journal of Dynamics and Differential Equations 4 Chaos 3 Transactions of the American Mathematical Society 3 Journal of Nonlinear Science 3 Journal of Physics A: Mathematical and Theoretical 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 2 Indiana University Mathematics Journal 2 Memoirs of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 Mathematical Physics Electronic Journal 2 Regular and Chaotic Dynamics 2 Annales Henri Poincaré 2 Discrete and Continuous Dynamical Systems. Series B 2 Discrete and Continuous Dynamical Systems. Series S 1 American Mathematical Monthly 1 Archive for Rational Mechanics and Analysis 1 Mathematische Zeitschrift 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Revista Matemática Iberoamericana 1 The Journal of Geometric Analysis 1 Expositiones Mathematicae 1 Journal of Knot Theory and its Ramifications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Experimental Mathematics 1 Mathematical Research Letters 1 Electronic Research Announcements of the American Mathematical Society 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Nonlinear Science and Numerical Simulation 1 La Gaceta de la Real Sociedad Matemática Española 1 Physical Review Letters 1 Communications on Pure and Applied Analysis 1 The IMA Volumes in Mathematics and its Applications 1 Proceedings of Symposia in Pure Mathematics 1 Networks and Heterogeneous Media 1 Journal of Modern Dynamics 1 Electronic Research Announcements in Mathematical Sciences all top 5 Fields 122 Dynamical systems and ergodic theory (37-XX) 50 Mechanics of particles and systems (70-XX) 21 Ordinary differential equations (34-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Partial differential equations (35-XX) 13 Numerical analysis (65-XX) 11 Global analysis, analysis on manifolds (58-XX) 8 Fluid mechanics (76-XX) 7 Differential geometry (53-XX) 6 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 4 Functional analysis (46-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Convex and discrete geometry (52-XX) 3 Manifolds and cell complexes (57-XX) 3 Probability theory and stochastic processes (60-XX) 3 Quantum theory (81-XX) 3 Biology and other natural sciences (92-XX) 2 Difference and functional equations (39-XX) 2 Computer science (68-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 139 Publications have been cited 1,838 times in 792 Documents Cited by ▼ Year ▼ Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation. Zbl 0603.58016De la Llave, R.; Marco, J. M.; Moriyon, R. 94 1986 The parameterization method for invariant manifolds. I: Manifolds associated to non-resonant subspaces. Zbl 1034.37016Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael 85 2003 The parameterization method for invariant manifolds. III: Overview and applications. Zbl 1101.37019Cabré, Xavier; Fontich, Ernest; de La Llave, Rafael 73 2005 The parameterization method for invariant manifolds. II: Regularity with respect to parameters. Zbl 1034.37017Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael 52 2003 A tutorial on KAM theory. Zbl 1055.37064de la Llave, Rafael 51 2001 A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results. Zbl 1102.37017Haro, A.; de la Llave, R. 50 2006 A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model. Zbl 1090.37044Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 48 2006 A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms. Zbl 1296.37048Haro, À.; de la Llave, R. 45 2006 KAM theory without action-angle variables. Zbl 1067.37081de la Llave, R.; González, A.; Jorba, À.; Villanueva, J. 44 2005 Relativistic stability of matter. I. Zbl 0602.58015Fefferman, C.; de la Llave, R. 44 1987 A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity. Zbl 1210.37062Haro, A.; de la Llave, R. 40 2007 A geometric approach to the existence of orbits with unbounded energy in generic periodic perturbations by a potential of generic geodesic flows of \(\mathbb{T}^2\). Zbl 0952.70015Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 36 2000 Planelike minimizers in periodic media. Zbl 1036.49040Caffarelli, Luis A.; de la Llave, Rafael 35 2001 Geometric properties of the scattering map of a normally hyperbolic invariant manifold. Zbl 1131.37032Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 34 2008 On squirt singularities in hydrodynamics. Zbl 1078.76018Córdoba, Diego; Fefferman, Charles; de la Llave, Rafael 31 2004 Regularity of the composition operator in spaces of Hölder functions. Zbl 0956.47029de la Llave, R.; Obaya, R. 30 1999 A KAM theory for conformally symplectic systems: efficient algorithms and their validation. Zbl 1345.37078Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 28 2013 Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems. Zbl 0770.58029de la Llave, R. 26 1992 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 25 2013 A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification. Zbl 1209.37008Calleja, Renato; de la Llave, Rafael 25 2010 KAM theory and a partial justification of Greene’s criterion for nontwist maps. Zbl 1049.37032Delshams, Amadeu; de la Llave, Rafael 25 2000 Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. Zbl 1209.37066Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 24 2009 Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media. Zbl 1152.35038de la Llave, Rafael; Valdinoci, Enrico 23 2007 On Irwin’s proof of the pseudostable manifold theorem. Zbl 0843.58100de la Llave, Rafael; Wayne, C. Eugene 22 1995 A rigorous partial justification of Green’s criterion. Zbl 0892.58045Falcolini, Corrado; de la Llave, R. 22 1992 Computation of whiskered invariant tori and their associated manifolds: new fast algorithms. Zbl 1279.70004Huguet, Gemma; de la Llave, Rafael; Sire, Yannick 21 2012 Cohomology equations near hyperbolic points and geometric versions of Sternberg linearization theorem. Zbl 0918.53016Banyaga, A.; de la Llave, R.; Wayne, C. E. 21 1996 Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems. Zbl 1230.37042de la Llave, Rafael; Windsor, Alistair 20 2010 Invariants for smooth conjugacy of hyperbolic dynamical systems. II. Zbl 0673.58036de la Llave, R. 19 1987 Topological methods in the instability problem of Hamiltonian systems. Zbl 1098.37056Gidea, Marian; de la Llave, Rafael 18 2006 Ground states and critical points for Aubry-Mather theory in Statistical mechanics. Zbl 1196.82095de la Llave, Rafael; Valdinoci, Enrico 17 2010 A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations. Zbl 1171.35372de la Llave, Rafael; Valdinoci, Enrico 17 2009 Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps. Zbl 1183.37014Calleja, Renato; de la Llave, Rafael 17 2009 Ground states and critical points for generalized Frenkel-Kontorova models in \(\mathbb Z^d\). Zbl 1206.82026de la Llave, Rafael; Valdinoci, Enrico 17 2007 Interfaces of ground states in Ising models with periodic coefficients. Zbl 1126.82305Caffarelli, Luis A.; de la Llave, Rafael 17 2005 Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349de la Llave, R.; Wayne, C. E. 17 2004 A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. Zbl 1370.65046Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael 16 2017 Existence of ideal knots. Zbl 1028.57008Gonzalez, O.; de la Llave, R. 16 2003 Invariant manifolds associated to nonresonant spectral subspaces. Zbl 0965.37028de la Llave, Rafael 16 1997 On the Aubry-Mather theory in statistical mechanics. Zbl 0917.46070Candel, A.; de la Llave, R. 15 1998 A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities. Zbl 1179.35340de la Llave, Rafael 14 2009 Geometric approaches to the problem of instability in Hamiltonian systems: an informal presentation. Zbl 1144.37022Delshams, Amadeu; Gidea, Marian; de la Llave, Rafael; Seara, Tere M. 14 2008 A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Zbl 1237.37040Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 13 2009 Manifolds on the verge of a hyperbolicity breakdown. Zbl 1144.37352Haro, À.; de la Llave, R. 13 2006 Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. Zbl 1091.37018Delshams, Amadeu; de La Llave, Rafael; Seara, Tere M. 13 2006 Lindstedt series for lower dimensional tori. Zbl 0961.37020Jorba, Àngel; de la Llave, Rafael; Zou, Maorong 13 1999 Aubry-Mather theory for functions on lattices. Zbl 0948.37015Koch, Hans; de la Llave, Rafael; Radin, Charles 13 1997 Invariants for smooth conjugacy of hyperbolic dynamical systems. IV. Zbl 0673.58038de la Llave, R.; Moriyón, R. 13 1988 Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case. Zbl 1407.34094He, Xiaolong; de la Llave, Rafael 12 2016 Construction of quasi-periodic solutions of delay differential equations via KAM techniques. Zbl 1184.34076Li, Xuemei; de la Llave, Rafael 12 2009 Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors. Zbl 0892.58066Falcolini, Corrado; de la Llave, R. 12 1992 A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results. Zbl 1068.37043Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 11 2003 Regularity of conjugacies between critical circle maps: an experimental study. Zbl 1116.37306de la Llave, Rafael; Petrov, Nikola P. 11 2002 Smooth dependence of thermodynamic limits of SRB-measures. Zbl 0956.37022Jiang, Miaohua; de la Llave, Rafael 11 2000 Accurate strategies for small divisor problems. Zbl 0739.58060De la Llave, R.; Rana, David 11 1990 Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices. Zbl 1351.37258Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 10 2015 Singularity theory for non-twist KAM tori. Zbl 1343.37043González-Enríquez, A.; Haro, A.; de la Llave, R. 10 2014 Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Zbl 1252.32015de la Llave, Rafael; Mireles James, Jason D. 10 2012 KAM theory for equilibrium states in 1-D statistical mechanics models. Zbl 1163.82002de la Llave, Rafael 10 2008 The parameterization method for one-dimensional invariant manifolds of higher-dimensional parabolic fixed points. Zbl 1123.37011Baldomá, Immaculada; Fontich, Ernest; de la Llave, Rafael; Martín, Pau 10 2007 Variational methods for quasi-periodic solutions of partial differential equations. Zbl 0987.35015de la Llave, Rafael 10 2000 Symmetry for a Dirichlet-Neumann problem arising in water waves. Zbl 1202.35066de la Llave, Rafael; Valdinoci, Enrico 9 2009 Analytic smoothing of geometric maps with applications to KAM theory. Zbl 1160.37024González-Enríquez, A.; de la Llave, R. 9 2008 Critical points inside the gaps of ground state laminations for some models in statistical mechanics. Zbl 1132.82010de la Llave, Rafael; Valdinoci, Enrico 9 2007 Gravity waves on the surface of the sphere. Zbl 0844.76008de la Llave, R.; Panayotaros, P. 9 1996 Accurate strategies for K. A. M. bounds and their implementation. Zbl 0747.65039De la Llave, R.; Rana, D. 9 1991 Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. Zbl 1370.65047Figueras, Jordi-Lluís; de la Llave, Rafael 8 2017 Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification. Zbl 1359.37121Capiński, Maciej J.; Gidea, Marian; de la Llave, Rafael 8 2017 Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion. Zbl 1355.37074Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 8 2016 Construction of response functions in forced strongly dissipative systems. Zbl 1339.70040Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 8 2013 KAM theory for quasi-periodic equilibria in one-dimensional quasi-periodic media. Zbl 1329.70046Su, Xifeng; de la Llave, Rafael 8 2012 Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation. Zbl 1205.82067Calleja, Renato; de la Llave, Rafael 8 2010 Further rigidity properties of conformal Anosov systems. Zbl 1087.37024De La Llave, R. 8 2004 An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations. Zbl 1407.37108de la Llave, Rafael; Sire, Yannick 7 2019 Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. Zbl 1343.37078de la Llave, R.; Mireles James, J. D. 7 2016 Barriers to transport and mixing in volume-preserving maps with nonzero flux. Zbl 1364.76066Fox, Adam M.; de la Llave, Rafael 7 2015 Local behavior near quasi-periodic solutions of conformally symplectic systems. Zbl 1274.70040Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 7 2013 Regularity of critical invariant circles of the standard nontwist map. Zbl 1074.37026Apte, A.; de la Llave, Rafael; Petrov, Nikola P. 7 2005 Analytic regularity of solutions of Livsic’s cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems. Zbl 0883.58024de la Llave, R. 7 1997 Perturbations of geodesic flows by recurrent dynamics. Zbl 1362.37116Gidea, Marian; de la Llave, Rafael 6 2017 The obstruction criterion for non-existence of invariant circles and renormalization. Zbl 1190.37046de la Llave, Rafael; Olvera, Arturo 6 2006 The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations. Zbl 1266.82014Blass, Timothy; de la Llave, Rafael 5 2013 Dynamical systems on lattices with decaying interaction. I: A functional analysis framework. Zbl 1213.37114Fontich, Ernest; de la Llave, Rafael; Martín, Pau 5 2011 A computer-assisted study of global dynamic transitions for a noninvertible system. Zbl 1185.37174Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; de la Llave, Rafael 5 2007 Rigidity of higher-dimensional conformal Anosov systems. Zbl 1028.37021de la Llave, Rafael 5 2002 Remarks on Sobolev regularity in Anosov systems. Zbl 1055.37030de la Llave, Rafael 5 2001 Cohomology equations and commutators of germs of contact diffeomorphisms. Zbl 0671.58031Banyaga, Augustin; de la Llave, Rafael; Wayne, C. Eugene 5 1989 Rates of convergence to equilibrium in the Prigogine-Misra-Courbage theory of irreversibility. Zbl 0511.60082de la Llave, R. 5 1982 Stable manifolds to bounded solutions in possibly ill-posed PDEs. Zbl 1448.35564Cheng, Hongyu; de la Llave, Rafael 4 2020 Response solutions for quasi-periodically forced, dissipative wave equations. Zbl 06764375Calleja, Renato C.; Celletti, Alessandra; Corsi, Livia; de la Llave, Rafael 4 2017 Resonant equilibrium configurations in quasi-periodic media: perturbative expansions. Zbl 1382.70022de la Llave, Rafael; Su, Xifeng; Zhang, Lei 4 2016 KAM tori and whiskered invariant tori for non-autonomous systems. Zbl 1364.37048Canadell, Marta; de la Llave, Rafael 4 2015 Fast iteration of cocycles over rotations and computation of hyperbolic bundles. Zbl 1308.70038Huguet, Gemma; de la Llave, Rafael; Sire, Yannick 4 2013 KAM theory for quasi-periodic equilibria in 1D quasi-periodic media. II: Long-range interactions. Zbl 1339.70041Su, Xifeng; de la Llave, Rafael 4 2012 Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations. Zbl 1226.82019de la Llave, Rafael; Luque, Alejandro 4 2011 Time-dependent scattering theory for ODEs and applications to reaction dynamics. Zbl 1223.34119Blazevski, Daniel; de la Llave, Rafael 4 2011 Smooth dependence on parameters of solutions to cohomology equations over Anosov systems with applications to cohomology equations on diffeomorphism groups. Zbl 1222.37025de la Llave, Rafael; Windsor, Alistair 4 2011 Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds. Zbl 1213.37115Fontich, Ernest; de la Llave, Rafael; Martín, Pau 4 2011 Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics. Zbl 1117.37031de la Llave, Rafael 4 2006 Linear response function for coupled hyperbolic attractors. Zbl 1084.37031Jiang, Miaohua; de la Llave, Rafael 4 2006 Stable manifolds to bounded solutions in possibly ill-posed PDEs. Zbl 1448.35564Cheng, Hongyu; de la Llave, Rafael 4 2020 A general mechanism of diffusion in Hamiltonian systems: qualitative results. Zbl 1437.37072Gidea, Marian; La Llave, Rafael De; M-Seara, Tere 2 2020 An a posteriori KAM theorem for whiskered tori in Hamiltonian partial differential equations with applications to some ill-posed equations. Zbl 1407.37108de la Llave, Rafael; Sire, Yannick 7 2019 Global persistence of Lyapunov subcenter manifolds as spectral submanifolds under dissipative perturbations. Zbl 07147390de la Llave, Rafael; Kogelbauer, Florian 1 2019 Global Melnikov theory in Hamiltonian systems with general time-dependent perturbations. Zbl 1405.37065Gidea, Marian; de la Llave, Rafael 1 2018 Uniform boundedness of iterates of analytic mappings implies linearization: a simple proof and extensions. Zbl 1402.32018de la Llave, Rafael 1 2018 A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations. Zbl 1370.65046Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael 16 2017 Numerical computations and computer assisted proofs of periodic orbits of the Kuramoto-Sivashinsky equation. Zbl 1370.65047Figueras, Jordi-Lluís; de la Llave, Rafael 8 2017 Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification. Zbl 1359.37121Capiński, Maciej J.; Gidea, Marian; de la Llave, Rafael 8 2017 Perturbations of geodesic flows by recurrent dynamics. Zbl 1362.37116Gidea, Marian; de la Llave, Rafael 6 2017 Response solutions for quasi-periodically forced, dissipative wave equations. Zbl 06764375Calleja, Renato C.; Celletti, Alessandra; Corsi, Livia; de la Llave, Rafael 4 2017 Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. I: Finitely differentiable, hyperbolic case. Zbl 1384.34080He, Xiaolong; de la Llave, Rafael 3 2017 Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems. Zbl 1425.70037Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 3 2017 Resonant equilibrium configurations in quasi-periodic media: KAM theory. Zbl 1404.70057de la Llave, Rafael; Su, Xifeng; Zhang, Lei 2 2017 Simple proofs and extensions of a result of L. D. Pustylnikov on the nonautonomous Siegel theorem. Zbl 1385.37022de la Llave, Rafael 1 2017 On the global dynamics of an electroencephalographic mean field model of the neocortex. Zbl 1382.35318Shirani, Farshad; Haddad, Wassim M.; de la Llave, Rafael 1 2017 A continuous family of equilibria in ferromagnetic media are ground states. Zbl 1376.82109Su, Xifeng; de la Llave, Rafael 1 2017 Construction of quasi-periodic solutions of state-dependent delay differential equations by the parameterization method. II: Analytic case. Zbl 1407.34094He, Xiaolong; de la Llave, Rafael 12 2016 Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion. Zbl 1355.37074Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 8 2016 Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. Zbl 1343.37078de la Llave, R.; Mireles James, J. D. 7 2016 Resonant equilibrium configurations in quasi-periodic media: perturbative expansions. Zbl 1382.70022de la Llave, Rafael; Su, Xifeng; Zhang, Lei 4 2016 Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices. Zbl 1351.37258Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 10 2015 Barriers to transport and mixing in volume-preserving maps with nonzero flux. Zbl 1364.76066Fox, Adam M.; de la Llave, Rafael 7 2015 KAM tori and whiskered invariant tori for non-autonomous systems. Zbl 1364.37048Canadell, Marta; de la Llave, Rafael 4 2015 Singularity theory for non-twist KAM tori. Zbl 1343.37043González-Enríquez, A.; Haro, A.; de la Llave, R. 10 2014 Localized stable manifolds for whiskered tori in coupled map lattices with decaying interaction. Zbl 1304.37020Blazevski, Daniel; de la Llave, Rafael 3 2014 An extension of Greene’s criterion for conformally symplectic systems and a partial justification. Zbl 1341.37031Calleja, Renato C.; Celletti, Alessandra; Falcolini, Corrado; de la Llave, Rafael 2 2014 A KAM theory for conformally symplectic systems: efficient algorithms and their validation. Zbl 1345.37078Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 28 2013 Computation of limit cycles and their isochrons: fast algorithms and their convergence. Zbl 1291.37108Huguet, Gemma; de la Llave, Rafael 25 2013 Construction of response functions in forced strongly dissipative systems. Zbl 1339.70040Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 8 2013 Local behavior near quasi-periodic solutions of conformally symplectic systems. Zbl 1274.70040Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael 7 2013 The analyticity breakdown for Frenkel-Kontorova models in quasi-periodic media: numerical explorations. Zbl 1266.82014Blass, Timothy; de la Llave, Rafael 5 2013 Fast iteration of cocycles over rotations and computation of hyperbolic bundles. Zbl 1308.70038Huguet, Gemma; de la Llave, Rafael; Sire, Yannick 4 2013 Computation of whiskered invariant tori and their associated manifolds: new fast algorithms. Zbl 1279.70004Huguet, Gemma; de la Llave, Rafael; Sire, Yannick 21 2012 Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps. Zbl 1252.32015de la Llave, Rafael; Mireles James, Jason D. 10 2012 KAM theory for quasi-periodic equilibria in one-dimensional quasi-periodic media. Zbl 1329.70046Su, Xifeng; de la Llave, Rafael 8 2012 KAM theory for quasi-periodic equilibria in 1D quasi-periodic media. II: Long-range interactions. Zbl 1339.70041Su, Xifeng; de la Llave, Rafael 4 2012 Invariant manifolds for analytic difference equations. Zbl 1260.39008de la Llave, Rafael; Lomelí, Héctor E. 3 2012 Percival Lagrangian approach to the Aubry-Mather theory. Zbl 1337.70037Su, Xifeng; de la Llave, Rafael 3 2012 Tracing KAM tori in presymplectic dynamical systems. Zbl 1327.70014Alishah, Hassan Najafi; de la Llave, Rafael 1 2012 Dynamical systems on lattices with decaying interaction. I: A functional analysis framework. Zbl 1213.37114Fontich, Ernest; de la Llave, Rafael; Martín, Pau 5 2011 Differentiability at the tip of Arnold tongues for Diophantine rotations: numerical studies and renormalization group explanations. Zbl 1226.82019de la Llave, Rafael; Luque, Alejandro 4 2011 Time-dependent scattering theory for ODEs and applications to reaction dynamics. Zbl 1223.34119Blazevski, Daniel; de la Llave, Rafael 4 2011 Smooth dependence on parameters of solutions to cohomology equations over Anosov systems with applications to cohomology equations on diffeomorphism groups. Zbl 1222.37025de la Llave, Rafael; Windsor, Alistair 4 2011 Dynamical systems on lattices with decaying interaction. II: Hyperbolic sets and their invariant manifolds. Zbl 1213.37115Fontich, Ernest; de la Llave, Rafael; Martín, Pau 4 2011 Combination laws for scaling exponents and relation to the geometry of renormalization operators. Zbl 1242.82017de la Llave, Rafael; Olvera, Arturo; Petrov, Nikola P. 2 2011 \(L^p\)-bounds for quasi-geostrophic equations via functional analysis. Zbl 1272.35165de la Llave, Rafael; Valdinoci, Enrico 1 2011 A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification. Zbl 1209.37008Calleja, Renato; de la Llave, Rafael 25 2010 Livšic theorems for non-commutative groups including diffeomorphism groups and results on the existence of conformal structures for Anosov systems. Zbl 1230.37042de la Llave, Rafael; Windsor, Alistair 20 2010 Ground states and critical points for Aubry-Mather theory in Statistical mechanics. Zbl 1196.82095de la Llave, Rafael; Valdinoci, Enrico 17 2010 Computation of the breakdown of analyticity in statistical mechanics models: Numerical results and a renormalization group explanation. Zbl 1205.82067Calleja, Renato; de la Llave, Rafael 8 2010 Convergence of differentiable functions on closed sets and remarks on the proofs of the “converse approximation lemmas”. Zbl 1223.26027Li, Xuemei; de la Llave, Rafael 3 2010 Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. Zbl 1209.37066Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 24 2009 A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations. Zbl 1171.35372de la Llave, Rafael; Valdinoci, Enrico 17 2009 Fast numerical computation of quasi-periodic equilibrium states in 1D statistical mechanics, including twist maps. Zbl 1183.37014Calleja, Renato; de la Llave, Rafael 17 2009 A smooth center manifold theorem which applies to some ill-posed partial differential equations with unbounded nonlinearities. Zbl 1179.35340de la Llave, Rafael 14 2009 A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems. Zbl 1237.37040Fontich, Ernest; de la Llave, Rafael; Sire, Yannick 13 2009 Construction of quasi-periodic solutions of delay differential equations via KAM techniques. Zbl 1184.34076Li, Xuemei; de la Llave, Rafael 12 2009 Symmetry for a Dirichlet-Neumann problem arising in water waves. Zbl 1202.35066de la Llave, Rafael; Valdinoci, Enrico 9 2009 An application of topological multiple recurrence to tiling. Zbl 1175.37023de la Llave, Rafael; Windsor, A. 1 2009 Geometric properties of the scattering map of a normally hyperbolic invariant manifold. Zbl 1131.37032Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 34 2008 Geometric approaches to the problem of instability in Hamiltonian systems: an informal presentation. Zbl 1144.37022Delshams, Amadeu; Gidea, Marian; de la Llave, Rafael; Seara, Tere M. 14 2008 KAM theory for equilibrium states in 1-D statistical mechanics models. Zbl 1163.82002de la Llave, Rafael 10 2008 Analytic smoothing of geometric maps with applications to KAM theory. Zbl 1160.37024González-Enríquez, A.; de la Llave, R. 9 2008 Boundaries of Siegel disks: numerical studies of their dynamics and regularity. Zbl 1309.37045de la Llave, Rafael; Petrov, Nikola P. 3 2008 Renormalization of arbitrary weak noises for one-dimensional critical dynamical systems: summary of results and numerical explorations. Zbl 1153.37022Díaz-Espinosa, Oliver; de la Llave, Rafael 1 2008 A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity. Zbl 1210.37062Haro, A.; de la Llave, R. 40 2007 Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media. Zbl 1152.35038de la Llave, Rafael; Valdinoci, Enrico 23 2007 Ground states and critical points for generalized Frenkel-Kontorova models in \(\mathbb Z^d\). Zbl 1206.82026de la Llave, Rafael; Valdinoci, Enrico 17 2007 The parameterization method for one-dimensional invariant manifolds of higher-dimensional parabolic fixed points. Zbl 1123.37011Baldomá, Immaculada; Fontich, Ernest; de la Llave, Rafael; Martín, Pau 10 2007 Critical points inside the gaps of ground state laminations for some models in statistical mechanics. Zbl 1132.82010de la Llave, Rafael; Valdinoci, Enrico 9 2007 A computer-assisted study of global dynamic transitions for a noninvertible system. Zbl 1185.37174Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; de la Llave, Rafael 5 2007 Universal scalings of universal scaling exponents. Zbl 1114.37022de la Llave, Rafael; Olvera, Arturo; Petrov, Nikola P. 3 2007 Renormalization and central limit theorem for critical dynamical systems with weak external noise. Zbl 1130.37022Díaz-Espinosa, Oliver; de la Llave, Rafael 1 2007 A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: rigorous results. Zbl 1102.37017Haro, A.; de la Llave, R. 50 2006 A geometric mechanism for diffusion in Hamiltonian systems overcoming in the large gap problem: Heuristics and rigorous verification on a model. Zbl 1090.37044Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 48 2006 A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms. Zbl 1296.37048Haro, À.; de la Llave, R. 45 2006 Topological methods in the instability problem of Hamiltonian systems. Zbl 1098.37056Gidea, Marian; de la Llave, Rafael 18 2006 Manifolds on the verge of a hyperbolicity breakdown. Zbl 1144.37352Haro, À.; de la Llave, R. 13 2006 Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. Zbl 1091.37018Delshams, Amadeu; de La Llave, Rafael; Seara, Tere M. 13 2006 The obstruction criterion for non-existence of invariant circles and renormalization. Zbl 1190.37046de la Llave, Rafael; Olvera, Arturo 6 2006 Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics. Zbl 1117.37031de la Llave, Rafael 4 2006 Linear response function for coupled hyperbolic attractors. Zbl 1084.37031Jiang, Miaohua; de la Llave, Rafael 4 2006 Invariant pre-foliations for non-resonant non-uniformly hyperbolic systems. Zbl 1080.37022Fontich, Ernest; de la Llave, Rafael; Martín, Pau 2 2006 The parameterization method for invariant manifolds. III: Overview and applications. Zbl 1101.37019Cabré, Xavier; Fontich, Ernest; de La Llave, Rafael 73 2005 KAM theory without action-angle variables. Zbl 1067.37081de la Llave, R.; González, A.; Jorba, À.; Villanueva, J. 44 2005 Interfaces of ground states in Ising models with periodic coefficients. Zbl 1126.82305Caffarelli, Luis A.; de la Llave, Rafael 17 2005 Regularity of critical invariant circles of the standard nontwist map. Zbl 1074.37026Apte, A.; de la Llave, Rafael; Petrov, Nikola P. 7 2005 On the regularity of integrable conformal structures invariant under Anosov systems. Zbl 1072.37026de la Llave, Rafael; Sadovskaya, Victoria 1 2005 On squirt singularities in hydrodynamics. Zbl 1078.76018Córdoba, Diego; Fefferman, Charles; de la Llave, Rafael 31 2004 Whiskered and low dimensional tori in nearly integrable Hamiltonian systems. Zbl 1136.37349de la Llave, R.; Wayne, C. E. 17 2004 Further rigidity properties of conformal Anosov systems. Zbl 1087.37024De La Llave, R. 8 2004 The parameterization method for invariant manifolds. I: Manifolds associated to non-resonant subspaces. Zbl 1034.37016Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael 85 2003 The parameterization method for invariant manifolds. II: Regularity with respect to parameters. Zbl 1034.37017Cabré, Xavier; Fontich, Ernest; De La Llave, Rafael 52 2003 Existence of ideal knots. Zbl 1028.57008Gonzalez, O.; de la Llave, R. 16 2003 A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results. Zbl 1068.37043Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. 11 2003 Invariant manifolds associated to invariant subspaces without invariant complements: a graph transform approach. Zbl 1115.37019de la Llave, R. 4 2003 Torus maps and the problem of a one-dimensional optical resonator with a quasiperiodically moving wall. Zbl 1027.78010Petrov, Nikola P.; de la Llave, Rafael; Vano, John A. 2 2003 Regularity of conjugacies between critical circle maps: an experimental study. Zbl 1116.37306de la Llave, Rafael; Petrov, Nikola P. 11 2002 Rigidity of higher-dimensional conformal Anosov systems. Zbl 1028.37021de la Llave, Rafael 5 2002 ...and 39 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 831 Authors 77 de la Llave, Rafael 24 Valdinoci, Enrico 18 James, J. D. Mireles 15 Haller, George 15 Haro, Àlex 14 Lessard, Jean-Philippe 13 Celletti, Alessandra 13 Fontich, Ernest 13 M-Seara, Tere 12 Delshams, Amadeu 11 Martín, Pau 11 Meiss, James D. 10 Calleja, Renato C. 10 Gidea, Marian 10 Mireles-James, Jason D. 9 Figueras, Jordi-Lluís 9 Katok, Anatole B. 9 Luque, Alejandro 9 Villanueva, Jordi 8 Gentile, Guido 8 Kaloshin, Vadim Yu. 8 Rabinowitz, Paul Henry 8 van den Berg, Jan Bouwe 7 Braides, Andrea 7 Capinski, Maciej J. 7 Chae, Dongho 7 Falcolini, Corrado 7 Lieb, Elliott H. 7 Paternain, Gabriel Pedro 7 Sadovskaya, Victoria 7 Zgliczyński, Piotr 6 Bolotin, Sergeĭ Vladimirovich 6 Castelli, Roberto 6 Chierchia, Luigi 6 Kalinin, Boris 6 Koch, Hans-Friedrich 6 Li, Xuemei 6 Qin, Wenxin 6 Wiggins, Stephen 5 Arioli, Gianni 5 Bach, Volker 5 Backes, Lucas H. 5 Breden, Maxime 5 Caffarelli, Luis Ángel 5 Cicalese, Marco 5 Cozzi, Matteo 5 Damjanović, Danijela 5 Gogolev, Andrey 5 Kim, Panki 5 Krauskopf, Bernd 5 Lu, Kening 5 Mezić, Igor 5 Novaga, Matteo 5 Obaya, Rafael 5 Osinga, Hinke Maria 5 Pollicott, Mark 5 Qiu, Hua 5 Su, Xifeng 5 Tompaidis, Stathis 5 Turaev, Dmitry V. 5 Wang, Yanan 5 Yao, Zhengan 5 Zhang, Weinian 5 Zhang, Wenmeng 5 Zhao, Kun 4 Apte, Amit 4 Asaoka, Masayuki 4 Baldomá, Inmaculada 4 Bessa, Mário 4 Chen, Zhen-Qing 4 Corsi, Livia 4 Dairbekov, Nurlan S. 4 Dipierro, Serena 4 Du, Yi 4 ElBialy, Mohamed Sami 4 Gameiro, Marcio F. 4 Guardia, Marcel 4 Huguet, Gemma 4 Jiang, Miaohua 4 Kocsard, Alejandro 4 Morrison, Philipp J. 4 Mramor, Blaz 4 Panayotaros, Panayotis 4 Peralta-Salas, Daniel 4 Rom-Kedar, Vered 4 Sevryuk, Mikhail Borisovich 4 Simó, Carles 4 Sire, Yannick 4 Song, Renming 4 von der Mosel, Heiko 4 Wayne, C. Eugene 4 Xu, Junxiang 3 Ambrose, David M. 3 Banyaga, Augustin 3 Bernard, Patrick 3 Blazevski, Daniel 3 Breunung, Thomas 3 Broer, Henk W. 3 Byeon, Jaeyoung 3 Canadell, Marta ...and 731 more Authors all top 5 Cited in 165 Serials 57 Communications in Mathematical Physics 57 Journal of Differential Equations 44 Physica D 27 Ergodic Theory and Dynamical Systems 25 Chaos 24 SIAM Journal on Applied Dynamical Systems 22 Journal of Statistical Physics 19 Regular and Chaotic Dynamics 18 Journal of Nonlinear Science 17 Journal of Dynamics and Differential Equations 17 Discrete and Continuous Dynamical Systems 16 Journal of Mathematical Physics 14 Archive for Rational Mechanics and Analysis 14 Transactions of the American Mathematical Society 13 Celestial Mechanics and Dynamical Astronomy 12 Nonlinearity 12 Advances in Mathematics 12 Journal of Functional Analysis 11 Communications in Nonlinear Science and Numerical Simulation 10 Mathematische Zeitschrift 9 Proceedings of the American Mathematical Society 8 Israel Journal of Mathematics 8 Calculus of Variations and Partial Differential Equations 7 Inventiones Mathematicae 7 Bulletin of the American Mathematical Society. New Series 7 Indagationes Mathematicae. New Series 7 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Experimental Mathematics 7 Annals of Mathematics. Second Series 6 Chaos, Solitons and Fractals 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 The Journal of Geometric Analysis 6 SIAM Journal on Mathematical Analysis 6 Qualitative Theory of Dynamical Systems 5 Duke Mathematical Journal 5 Mathematische Annalen 5 Nonlinear Dynamics 5 Annales Henri Poincaré 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of Modern Dynamics 4 Journal of Mathematical Analysis and Applications 4 Annales de l’Institut Fourier 4 Geometric and Functional Analysis. GAFA 4 Journal of Difference Equations and Applications 4 Electronic Research Announcements of the American Mathematical Society 4 Physical Review Letters 4 Dynamical Systems 4 Journal of Computational Dynamics 3 Applicable Analysis 3 Communications on Pure and Applied Mathematics 3 Journal of Computational Physics 3 Journal of Mathematical Biology 3 Acta Mathematica 3 Journal of Computational and Applied Mathematics 3 Topology and its Applications 3 Journal of Economic Dynamics & Control 3 Boletim da Sociedade Brasileira de Matemática. Nova Série 3 Journal of Knot Theory and its Ramifications 3 Communications in Contemporary Mathematics 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Computers & Mathematics with Applications 2 Journal d’Analyse Mathématique 2 Physics Reports 2 Reviews of Modern Physics 2 Mathematics of Computation 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Geometriae Dedicata 2 Publications Mathématiques 2 Journal of Approximation Theory 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Systems & Control Letters 2 Journal of Complexity 2 Applications of Mathematics 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Continuum Mechanics and Thermodynamics 2 Potential Analysis 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Foundations of Computational Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Milan Journal of Mathematics 2 Advances in Difference Equations 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Fixed Point Theory and Applications 2 Frontiers of Mathematics in China 2 Discrete and Continuous Dynamical Systems. Series S 2 Analysis & PDE 2 Journal of Geometric Mechanics 2 Science China. Mathematics 2 Molecular Based Mathematical Biology 2 Journal of Function Spaces 2 Computational and Mathematical Biophysics 1 Biological Cybernetics 1 Mathematical Methods in the Applied Sciences 1 Mathematical Notes ...and 65 more Serials all top 5 Cited in 49 Fields 507 Dynamical systems and ergodic theory (37-XX) 167 Partial differential equations (35-XX) 151 Mechanics of particles and systems (70-XX) 106 Ordinary differential equations (34-XX) 71 Numerical analysis (65-XX) 67 Differential geometry (53-XX) 65 Statistical mechanics, structure of matter (82-XX) 54 Fluid mechanics (76-XX) 43 Global analysis, analysis on manifolds (58-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 35 Manifolds and cell complexes (57-XX) 32 Operator theory (47-XX) 29 Quantum theory (81-XX) 20 Probability theory and stochastic processes (60-XX) 20 Biology and other natural sciences (92-XX) 15 Mechanics of deformable solids (74-XX) 13 Functional analysis (46-XX) 11 Topological groups, Lie groups (22-XX) 11 General topology (54-XX) 10 Real functions (26-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 6 Functions of a complex variable (30-XX) 5 Difference and functional equations (39-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Approximations and expansions (41-XX) 4 Computer science (68-XX) 4 Geophysics (86-XX) 3 Number theory (11-XX) 3 Algebraic geometry (14-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 3 Integral equations (45-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 3 Optics, electromagnetic theory (78-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 General and overarching topics; collections (00-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Relativity and gravitational theory (83-XX) 2 Astronomy and astrophysics (85-XX) 1 Combinatorics (05-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Geometry (51-XX) 1 Statistics (62-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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