Edit Profile (opens in new tab) Ratiu, Tudor Stefan Compute Distance To: Compute Author ID: ratiu.tudor-stefan Published as: Ratiu, Tudor S.; Ratiu, Tudor; Ratiu, T. S.; Ratiu, T.; Ratiu, Tudor Stefan Homepage: http://math.sjtu.edu.cn/faculty/show.php?id=153 External Links: MGP · ORCID · Wikidata · ResearchGate · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 233 Publications since 1972, including 15 Books 15 Contributions as Editor Reviewing Activity: 82 Reviews Biographic References: 1 Publication Co-Authors: 133 Co-Authors with 235 Joint Publications 2,753 Co-Co-Authors all top 5 Co-Authors 13 single-authored 45 Marsden, Jerrold Eldon 32 Gay-Balmaz, François 23 Ortega, Juan-Pablo 20 Bloch, Anthony Michael 20 Holm, Darryl D. 11 Smolyanov, Oleg Georgievich 8 Castrillón López, Marco 8 Flaschka, Hermann 8 Lewis, Debra 8 Schmid, Rudolf 8 Weinstein, Alan David 7 Birtea, Petre 7 Gough, John E. 7 Jotz, Madeleine 6 Cendra, Hernán 6 Chechkin, Gregory Aleksandrovich 6 Pelayo, Alvaro 5 Adams, Malcolm R. 5 Demoures, François 5 Krishnaprasad, P.s. 5 Montgomery, Richard 5 Odzijewicz, Anatol 5 Raugel, Geneviève 4 Bao, David 4 Puta, Mircea 4 Tronci, Cesare 4 Tudoran, Răzvan Micu 3 Beltiţă, Daniel 3 Brockett, Roger Ware 3 Busuioc, Adriana Valentina 3 Chossat, Pascal 3 Derks, Gianne 3 Desbrun, Mathieu 3 Eliashberg, Yakov Matveevich 3 Newell, Alan C. 3 Nguyen Tien Zung 3 Perlmutter, Matthew 3 Romanov, Maksim S. 3 Samokhin, Vyacheslav N. 3 Scheurle, Jürgen 2 Abraham, Ralph Herman 2 Brînzănescu, Vasile 2 Craioveanu, Mircea-Eugen 2 Crouch, Peter E. 2 Dobrogowska, Alina 2 Drăgulete, Oana M. 2 Ellis, David C. P. 2 Martín de Diego, David 2 Mazer, Arthur A. 2 Meier, David M. 2 Misiołek, Gerard 2 Montaldi, James A. 2 Muñoz Masqué, Jaime 2 Neeb, Karl-Hermann 2 Putkaradze, Vakhtang 2 Reghiş, Mircea 2 Shafarevich, Andreĭ Igorevich 2 Shkoller, Steve 2 Simo, Juan Carlos 2 Tarama, Daisuke 2 Vialard, François-Xavier 2 Vũ Ngọc, San 1 Abarbanel, Henry D. I. 1 Albu, Adrian C. 1 Aragón, Alejandro M. 1 Bernard, Peter S. 1 Blankenstein, Guido 1 Bruveris, Martins 1 Burghelea, Dan 1 Caşu, Ioan 1 Chang, Dong Eui 1 Chechkina, Tatiana P. 1 Chorin, Alexandre Joel 1 Cruzeiro, Ana-Bela 1 Dellnitz, Michael 1 Fassò, Francesco 1 Fernandes, Rui Loja 1 Filatova, T. A. 1 García Pérez, Pedro L. 1 Golubitsky, Martin A. 1 Gotay, Mark J. 1 Gualtieri, Marco 1 Guha, Partha 1 Hilgert, Joachim 1 Hochgerner, Simon 1 Hoppe, Jens 1 Hounkonnou, Mahouton Norbert 1 Huebschmann, Johannes 1 Isenberg, Jim 1 Iserles, Arieh 1 Jacobs, Henry O. 1 Keyfitz, Barbara Lee 1 Kobayashi, Toshiyuki 1 Kobilarov, Marin 1 Kodama, Yuji 1 Kozlov, Ivan Konstantinovich 1 Kupershmidt, Boris A. 1 Lafontaine, Jacques 1 Leyendecker, Sigrid 1 Li, Songhao ...and 42 more Co-Authors all top 5 Serials 11 Doklady Mathematics 10 Communications in Mathematical Physics 7 Nonlinearity 7 Journal of Geometry and Physics 7 Physica D 6 Letters in Mathematical Physics 5 Transactions of the American Mathematical Society 5 Journal of Nonlinear Science 4 Archive for Rational Mechanics and Analysis 4 Differential Geometry and its Applications 4 The Journal of Symplectic Geometry 4 Journal of Geometric Mechanics 3 Journal of Mathematical Physics 3 Reports on Mathematical Physics 3 Advances in Mathematics 3 American Journal of Mathematics 3 Journal of Differential Equations 3 Journal of Functional Analysis 3 Mathematische Annalen 3 Advances in Applied Mathematics 3 Oberwolfach Reports 3 Monografii Matematice (Timișoara) 2 Analele Universității din Timișoara. Științe Matematice 2 Annales de l’Institut Fourier 2 Geometriae Dedicata 2 Inventiones Mathematicae 2 Memoirs of the American Mathematical Society 2 Annals of Global Analysis and Geometry 2 IMRN. International Mathematics Research Notices 2 Geometric and Functional Analysis. GAFA 2 Journal of Dynamics and Differential Equations 2 Journal of Mathematical Sciences (New York) 2 Journal of Lie Theory 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Communications in Mathematical Sciences 2 Dynamics of Partial Differential Equations 2 Fields Institute Communications 2 Lecture Notes in Mathematics 2 Proceedings of the Steklov Institute of Mathematics 2 Progress in Mathematics 2 Texts in Applied Mathematics 2 Journal of Physics A: Mathematical and Theoretical 1 Applicable Analysis 1 Classical and Quantum Gravity 1 Computer Methods in Applied Mechanics and Engineering 1 Physics Letters. A 1 Physics Reports 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Duke Mathematical Journal 1 Indiana University Mathematics Journal 1 Mathematische Zeitschrift 1 Numerische Mathematik 1 Pacific Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Ser. A 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Control and Optimization 1 Libertas Mathematica 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of the American Mathematical Society 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 L’Enseignement Mathématique. 2e Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Russian Journal of Mathematical Physics 1 Mathematical Research Letters 1 Sbornik: Mathematics 1 Transformation Groups 1 Mathematics and Mechanics of Solids 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Journal of Mathematical Fluid Mechanics 1 Regular and Chaotic Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Contemporary Mathematics 1 Journal of Nonlinear Mathematical Physics 1 Moscow Mathematical Journal 1 Bulletin of the Brazilian Mathematical Society. New Series 1 Analysis and Applications (Singapore) 1 International Journal of Geometric Methods in Modern Physics 1 Chebyshevskiĭ Sbornik 1 Applied Mathematical Sciences 1 Lectures in Applied Mathematics 1 London Mathematical Society Lecture Note Series 1 Mathematical Sciences Research Institute Publications 1 Geometry and Topology Monographs 1 Forum of Mathematics, Sigma 1 Research in the Mathematical Sciences 1 Translations. Series 2. American Mathematical Society all top 5 Fields 110 Dynamical systems and ergodic theory (37-XX) 88 Mechanics of particles and systems (70-XX) 86 Differential geometry (53-XX) 52 Global analysis, analysis on manifolds (58-XX) 41 Fluid mechanics (76-XX) 30 Partial differential equations (35-XX) 25 Topological groups, Lie groups (22-XX) 20 Nonassociative rings and algebras (17-XX) 16 Quantum theory (81-XX) 15 General and overarching topics; collections (00-XX) 14 Functional analysis (46-XX) 13 Mechanics of deformable solids (74-XX) 9 Ordinary differential equations (34-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Manifolds and cell complexes (57-XX) 8 Statistical mechanics, structure of matter (82-XX) 5 History and biography (01-XX) 5 Numerical analysis (65-XX) 5 Systems theory; control (93-XX) 3 Algebraic geometry (14-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Operator theory (47-XX) 3 Probability theory and stochastic processes (60-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 General topology (54-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 196 Publications have been cited 3,897 times in 2,563 Documents Cited by ▼ Year ▼ Manifolds, tensor analysis, and applications. 2nd ed. Zbl 0875.58002Abraham, R.; Marsden, J. E.; Ratiu, T. 469 1988 Introduction to mechanics and symmetry. A basic exposition of classical mechanical systems. 2nd ed. Zbl 0933.70003Marsden, Jerrold E.; Ratiu, Tudor S. 334 1999 The Euler-Poincaré equations and semidirect products with applications to continuum theories. Zbl 0951.37020Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 294 1998 Nonlinear stability of fluid and plasma equilibria. Zbl 0717.76051Holm, D. D.; Marsden, J. E.; Ratiu, T.; Weinstein, A. 227 1985 Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems. Zbl 0811.70002Marsden, Jerrold E.; Ratiu, Tudor S. 142 1994 Momentum maps and Hamiltonian reduction. Zbl 1241.53069Ortega, Juan-Pablo; Ratiu, Tudor S. 124 2004 Reduction of Poisson manifolds. Zbl 0602.58016Marsden, Jerrold E.; Ratiu, Tudor 102 1986 Manifolds, tensor analysis, and applications. Zbl 0508.58001Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor 91 1983 Semidirect products and reduction in mechanics. Zbl 0529.58011Marsden, Jerrold E.; Ratiu, Tudor; Weinstein, Alan 88 1984 Reduction, symmetry, and phases in mechanics. Zbl 0713.58052Marsden, J. E.; Montgomery, R.; Ratiu, T. 73 1990 Hamiltonian reduction by stages. Zbl 1129.37001Marsden, Jerrold E.; Misiołek, Gerard; Ortega, Juan-Pablo; Perlmutter, Matthew; Ratiu, Tudor S. 68 2007 Lagrangian reduction by stages. Zbl 1193.37072Cendra, Hernán; Marsden, Jerrold E.; Ratiu, Tudor S. 67 2001 The Euler-Poincaré equations and double bracket dissipation. Zbl 0846.58048Bloch, Anthony; Krishnaprasad, P. S.; Marsden, Jerrold E.; Ratiu, Tudor S. 59 1996 Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\). Zbl 0643.35098Flaschka, H.; Newell, A. C.; Ratiu, T. 45 1983 The Hamiltonian structure for dynamic free boundary problems. Zbl 0638.58044Lewis, Debra; Marsden, J.; Montgomery, R.; Ratiu, T. 43 1986 The motion of the free \(n\)-dimensional rigid body. Zbl 0432.70011Ratiu, Tudor 42 1980 Reduction theory and the Lagrange-Routh equations. Zbl 1044.37043Marsden, Jerrold E.; Ratiu, Tudor S.; Scheurle, Jürgen 40 2000 The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. Zbl 1026.76004Busuioc, Adriana Valentina; Ratiu, Tudor S. 39 2003 The geometric structure of complex fluids. Zbl 1161.37052Gay-Balmaz, François; Ratiu, Tudor S. 36 2009 Completely integrable gradient flows. Zbl 0766.58027Bloch, Anthony M.; Brockett, Roger W.; Ratiu, Tudor S. 35 1992 Banach Lie-Poisson spaces and reduction. Zbl 1044.53057Odzijewicz, Anatol; Ratiu, Tudor S. 33 2003 Dissipation induced instabilities. Zbl 0834.58025Bloch, A. M.; Krishnaprasad, P. S.; Marsden, J. E.; Ratiu, T. S. 32 1994 Invariant higher-order variational problems. Zbl 1279.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 30 2012 Nonlinear stability analysis of stratified fluid equilibria. Zbl 0637.76119Abarbanel, H. D. I.; Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 29 1986 Geometric mechanics, Lagrangian reduction, and nonholonomic systems. Zbl 1021.37001Cendra, Hernán; Marsden, Jerrold E.; Ratiu, Tudor S. 28 2001 Gauged Lie-Poisson structures. Zbl 0546.58026Montgomery, Richard; Marsden, Jerrold; Ratiu, Tudor 28 1984 The Hamiltonian structure of continuum mechanics in material, inverse material, spatial and convective representations. Zbl 0611.70015Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 27 1986 Hamiltonian systems with symmetry, coadjoint orbits and plasma physics. Zbl 0577.58013Marsden, J. E.; Weinstein, A.; Ratiu, T.; Schmid, R.; Spencer, R. G. 26 1983 The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. Zbl 0979.58004Marsden, J. E.; Ratiu, T. S.; Shkoller, S. 25 2000 Euler-Poincaré reduction on principal bundles. Zbl 1020.58018Castrillón López, M.; García Pérez, P. L.; Ratiu, T. S. 25 2001 The differentiable structure of three remarkable diffeomorphism groups. Zbl 0451.58011Ratiu, Tudor; Schmid, Rudolf 25 1981 Reduction in principal fiber bundles: Covariant Euler-Poincaré equations. Zbl 0967.53019Castrillón López, Marco; Ratiu, Tudor S.; Shkoller, Steve 24 2000 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 24 2010 Stability of Hamiltonian relative equilibria. Zbl 0984.37063Ortega, Juan-Pablo; Ratiu, Tudor S. 24 1999 Reduction in principal bundles: covariant Lagrange-Poincaré equations. Zbl 1037.53056Castrillón López, M.; Ratiu, T. S. 24 2003 The momentum map representation of images. Zbl 1211.58010Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 23 2011 Variational principles for Lie-Poisson and Hamilton-Poincaré equations. Zbl 1156.37314Cendra, Hernan; Marsden, Jerrold E.; Pekarsky, Sergey; Ratiu, Tudor S. 23 2003 The heavy top: A geometric treatment. Zbl 0753.70004Lewis, Debra; Ratiu, T.; Simo, J. C.; Marsden, J. E. 21 1992 A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra. Zbl 0715.58004Bloch, A. M.; Flaschka, H.; Ratiu, T. 20 1990 Lagrangian reduction, the Euler-Poincaré equations, and semidirect products. Zbl 0989.37052Cendra, Hernán; Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 19 1998 A convexity theorem for Poisson actions of compact Lie groups. Zbl 0877.58025Flaschka, Hermann; Ratiu, Tudor 19 1996 Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body. Zbl 0509.58026Ratiu, Tudor 19 1982 The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation. Zbl 1320.32018Gay-Balmaz, François; Ratiu, Tudor S. 19 2015 The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits. Zbl 1120.22007Beltiţă, Daniel; Ratiu, Tudor S.; Tumpach, Alice Barbara 18 2007 A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map. Zbl 0715.58033Bloch, Anthony M.; Brockett, Roger W.; Ratiu, Tudor S. 17 1990 Clebsch optimal control formulation in mechanics. Zbl 1233.49005Gay-Balmaz, François; Ratiu, Tudor S. 17 2011 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 17 2011 A crash course in geometric mechanics. (Notes of the courses given by Tudor Ratiu). Zbl 1159.70001Ratiu, T. S.; Tudoran, R.; Sbano, L.; Sousa Dias, E.; Terra, G. 17 2005 Singular reduction of implicit Hamiltonian systems. Zbl 1065.37040Blankenstein, Guido; Ratiu, Tudor S. 16 2004 Singular reduction of Poisson manifolds. Zbl 0989.37070Ortega, Juan-Pablo; Ratiu, Tudor S. 16 1998 The momentum map in Poisson geometry. Zbl 1180.53083Fernandes, Rui Loja; Ortega, Juan-Pablo; Ratiu, Tudor S. 16 2009 Rotating \(n\)-gon/\(kn\)-gon vortex configurations. Zbl 0869.76012Lewis, Debra; Ratiu, T. 15 1996 The Lagrange rigid body motion. Zbl 0466.58020Ratiu, Tudor; van Moerbeke, P. 15 1982 Discrete variational Lie group formulation of geometrically exact beam dynamics. Zbl 1315.53090Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, S.; Ratiu, T. S.; Weinand, Y. 15 2015 Symplectic connections and the linearisation of Hamiltonian systems. Zbl 0795.58018Marsden, J. E.; Ratiu, T.; Raugel, G. 15 1991 A new Lagrangian dynamic reduction in field theory. Zbl 1404.58029Gay-Balmaz, François; Ratiu, Tudor S. 15 2010 Nonlinear stability of singular relative periodic orbits in Hamiltonian systems with symmetry. Zbl 0955.37032Ortega, Juan-Pablo; Ratiu, Tudor S. 14 1999 Reduced variational formulations in free boundary continuum mechanics. Zbl 1260.37031Gay-Balmaz, François; Marsden, Jerrold E.; Ratiu, Tudor S. 14 2012 Invariant higher-order variational problems. II. Zbl 1351.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 14 2012 Stability and bifurcation of a rotating planar liquid drop. Zbl 0651.76021Lewis, Debra; Marsden, Jerrold Eldon; Ratiu, Tudor Stefan 14 1987 Reduction and Hamiltonian structures on duals of semidirect product Lie algebras. Zbl 0546.58025Marsden, Jerrold E.; Ratiu, Tudor; Weinstein, Alan 14 1984 The C. Neumann problem as a completely integrable system on an adjoint orbit. Zbl 0475.58006Ratiu, Tudor 14 1981 Symplectic reduction for semidirect products and central extensions. Zbl 0973.53069Marsden, Jerrold E.; Misiołek, Gerard; Perlmutter, Matthew; Ratiu, Tudor S. 13 1998 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 13 2018 Lagrange-Poincaré field equations. Zbl 1253.70031Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 12 2011 A symplectic slice theorem. Zbl 1072.53541Ortega, Juan-Pablo; Ratiu, Tudor S. 12 2002 Asymptotic and Lyapunov stability of constrained and Poisson equilibria. Zbl 1066.37017Ortega, Juan-Pablo; Planas-Bielsa, Víctor; Ratiu, Tudor S. 12 2005 On the nonlinear convexity theorem of Kostant. Zbl 0785.22019Lu, Jiang-Hua; Ratiu, Tudor 12 1991 The tropical momentum map: a classification of toric log symplectic manifolds. Zbl 1442.53057Gualtieri, Marco; Li, Songhao; Pelayo, Álvaro; Ratiu, Tudor S. 12 2017 The diameter of the symplectomorphism group is infinite. Zbl 0725.58006Eliashberg, Yakov; Ratiu, Tudor 11 1991 Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body. Zbl 1300.70005Birtea, Petre; Caşu, Ioan; Ratiu, Tudor S.; Turhan, Murat 11 2012 Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body. Zbl 0459.70007Ratiu, Tudor 11 1981 A Lie group structure for pseudodifferential operators. Zbl 0587.58047Adams, Malcolm; Ratiu, Tudor; Schmid, Rudolf 11 1986 Stability of rigid body motion using the energy-Casimir method. Zbl 0526.70025Holm, Darryl; Marsden, Jerrold; Ratiu, Tudor; Weinstein, Alan 11 1984 Dirac structures, nonholonomic systems and reduction. Zbl 1247.53096Jotz, Madeleine; Ratiu, T. S. 11 2012 On the geometry of the Virasoro-Bott group. Zbl 0945.58005Michor, P. W.; Ratiu, T. S. 10 1998 Hamiltonian structure and Lyapunov stability for ideal continuum dynamics. (Mathematical Seminar held at the University of Montréal, Canada, July 29 - August 16, 1985). Zbl 0594.00020Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 10 1986 The affine invariant of proper semitoric integrable systems. Zbl 1392.37046Pelayo, Álvaro; Ratiu, Tudor S.; Ngọc, San Vu 10 2017 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143Ratiu, T. S.; Smolyanov, O. G. 9 2013 A Lie group structure for Fourier integral operators. Zbl 0619.58010Adams, Malcolm; Ratiu, Tudor; Schmid, Rudolf 9 1986 Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids. Zbl 1149.70015Gay-Balmaz, François; Ratiu, Tudor S. 9 2008 Geometric representation theory for unitary groups of operator algebras. Zbl 1108.22008Beltiţă, Daniel; Ratiu, Tudor S. 8 2007 Singular reduction of Dirac structures. Zbl 1385.70039Jotz, M.; Ratiu, T. S.; Śniatycki, J. 8 2011 The optimal momentum map. Zbl 1015.53053Ortega, Juan-Pablo; Ratiu, Tudor S. 8 2002 A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus. Zbl 0806.22012Bloch, A. M.; Flaschka, H.; Ratiu, T. 8 1993 Involution theorems. Zbl 0435.58014Ratiu, Tudor 8 1980 Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 8 2009 Symplectic leaves in real Banach Lie-Poisson spaces. Zbl 1083.58011Beltiţă, D.; Ratiu, T. S. 8 2005 Kac-Moody Lie algebras and soliton equations. III: Stationary equations associated with \(A_ 1^{(1)}\). Zbl 0643.35099Flaschka, H.; Newell, A. C.; Ratiu, T. 8 1983 Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems. Zbl 1295.81097Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 7 2014 Multisymplectic variational integrators and space/time symplecticity. Zbl 1338.65271Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 7 2016 Equivalent theories of liquid crystal dynamics. Zbl 1361.76005Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 7 2013 Moduli spaces of toric manifolds. Zbl 1298.53088Pelayo, Á.; Pires, A. R.; Ratiu, T. S.; Sabatini, S. 7 2014 Geometry of non-holonomic diffusion. Zbl 1317.37064Hochgerner, Simon; Ratiu, Tudor S. 7 2015 Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\). Zbl 1473.70029Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S. 7 2014 Nematodynamics and random homogenization. Zbl 1349.76017Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S.; Romanov, Maksim S. 7 2016 Geometric dynamics of optimization. Zbl 1271.49003Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 7 2013 Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems. Zbl 1321.37054Bloch, Anthony M.; Morrison, Philip J.; Ratiu, Tudor S. 6 2013 Extensions of Banach Lie-Poisson spaces. Zbl 1067.53065Odzijewicz, Anatol; Ratiu, Tudor S. 6 2004 The symmetric representation of the rigid body equations and their discretization. Zbl 1064.70004Bloch, Anthony M.; Crouch, Peter E.; Marsden, Jerrold E.; Ratiu, Tudor S. 6 2002 Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type. Zbl 1460.53074Ratiu, Tudor S.; Tarama, Daisuke 1 2020 Presymplectic convexity and (ir)rational polytopes. Zbl 1462.53067Ratiu, Tudor; Nguyen, Tien Zung 3 2019 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 13 2018 The tropical momentum map: a classification of toric log symplectic manifolds. Zbl 1442.53057Gualtieri, Marco; Li, Songhao; Pelayo, Álvaro; Ratiu, Tudor S. 12 2017 The affine invariant of proper semitoric integrable systems. Zbl 1392.37046Pelayo, Álvaro; Ratiu, Tudor S.; Ngọc, San Vu 10 2017 The geometric nature of the Flaschka transformation. Zbl 1368.37065Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S. 3 2017 Coadjoint orbits in duals of Lie algebras with admissible ideals. Zbl 1402.53064Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S. 1 2017 Existence and uniqueness theorems for the full three-dimensional Ericksen-Leslie system. Zbl 1362.76004Chechkin, Gregory A.; Ratiu, Tudor S.; Romanov, Maxim S.; Samokhin, Vyacheslav N. 1 2017 Noether theorems and quantum anomalies. Zbl 1366.81260Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 1 2017 A multisymplectic integrator for elastodynamic frictionless impact problems. Zbl 1439.74234Demoures, François; Gay-Balmaz, François; Desbrun, Mathieu; Ratiu, Tudor S.; Aragón, Alejandro M. 1 2017 Multisymplectic variational integrators and space/time symplecticity. Zbl 1338.65271Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 7 2016 Nematodynamics and random homogenization. Zbl 1349.76017Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S.; Romanov, Maksim S. 7 2016 Multisymplectic variational integrators for nonsmooth Lagrangian continuum mechanics. Zbl 1416.65512Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 3 2016 Existence and uniqueness theorems for the two-dimensional Ericksen-Leslie system. Zbl 1346.76010Chechkin, Gregory A.; Ratiu, Tudor S.; Romanov, Maxim S.; Samokhin, Vyacheslav N. 3 2016 Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties. Zbl 1420.17026Hounkonnou, Mahouton Norbert; Guha, Partha; Ratiu, Tudor 1 2016 The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation. Zbl 1320.32018Gay-Balmaz, François; Ratiu, Tudor S. 19 2015 Discrete variational Lie group formulation of geometrically exact beam dynamics. Zbl 1315.53090Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, S.; Ratiu, T. S.; Weinand, Y. 15 2015 Geometry of non-holonomic diffusion. Zbl 1317.37064Hochgerner, Simon; Ratiu, Tudor S. 7 2015 Quantum anomalies and logarithmic derivatives of Feynman pseudomeasures. Zbl 1341.81038Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 4 2015 Fiber connectivity and bifurcation diagrams of almost toric integrable systems. Zbl 1335.37042Pelayo, Álvaro; Ratiu, Tudor S.; San Vũ Ngọc 4 2015 Wigner measures and quantum control. Zbl 1321.81030Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 3 2015 Noether’s theorem for dissipative quantum dynamical semi-groups. Zbl 1311.81161Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G. 3 2015 Existence and uniqueness theorems in two-dimensional nematodynamics. Finite speed of propagation. Zbl 1330.82055Ratiu, T. S.; Romanov, M. S.; Samokhin, V. N.; Chechkin, G. A. 2 2015 The \(U(n)\) free rigid body: integrability and stability analysis of the equilibria. Zbl 1378.70005Ratiu, Tudor S.; Tarama, Daisuke 2 2015 Integrable systems of Neumann type. Zbl 1338.37071Dobrogowska, Alina; Ratiu, Tudor S. 1 2015 Hamiltonian structures in the quantum theory of Hamilton-Dirac systems. Zbl 1337.81086Ratiu, T. S.; Smolyanov, O. G. 1 2015 Wigner quantization of Hamilton-Dirac systems. Zbl 1337.81082Ratiu, T. S.; Smolyanov, O. G. 1 2015 \(L^2\)-cohomology and complete Hamiltonian manifolds. Zbl 1304.53086Mazzeo, Rafe; Pelayo, Álvaro; Ratiu, Tudor S. 1 2015 Geometry, mechanics, and dynamics. The legacy of Jerry Marsden. Selected papers presented at a focus program, Fields Institute for Research in Mathematical Sciences, Toronto, Canada, July 2012. Zbl 1317.53004 1 2015 Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems. Zbl 1295.81097Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 7 2014 Moduli spaces of toric manifolds. Zbl 1298.53088Pelayo, Á.; Pires, A. R.; Ratiu, T. S.; Sabatini, S. 7 2014 Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\). Zbl 1473.70029Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S. 7 2014 Integrable \(G\)-strands on semisimple Lie groups. Zbl 1298.22012Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 1 2014 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143Ratiu, T. S.; Smolyanov, O. G. 9 2013 Equivalent theories of liquid crystal dynamics. Zbl 1361.76005Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 7 2013 Geometric dynamics of optimization. Zbl 1271.49003Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 7 2013 Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems. Zbl 1321.37054Bloch, Anthony M.; Morrison, Philip J.; Ratiu, Tudor S. 6 2013 Thin layer of a non-Newtonian fluid flowing on a rough surface and percolating through a perforated obstacle. Zbl 1268.76003Linkevich, A. Yu.; Ratiu, T. S.; Spiridonov, S. V.; Chechkin, G. A. 6 2013 Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold. Zbl 1292.81063Ratiu, T. S.; Suleimanova, A. A.; Shafarevich, A. I. 4 2013 Dirac optimal reduction. Zbl 1275.37028Jotz, M. M.; Ratiu, T. S. 4 2013 Extensions of Lie-Rinehart algebras and cotangent bundle reduction. Zbl 1304.53083Huebschmann, J.; Perlmutter, M.; Ratiu, T. S. 2 2013 On the coupling between an ideal fluid and immersed particles. Zbl 1302.76007Jacobs, Henry O.; Ratiu, Tudor S.; Desbrun, Mathieu 2 2013 Representations of Lie groups and supergroups. Abstracts from the workshop held March 10–16, 2013. Zbl 1349.00189 1 2013 Invariant higher-order variational problems. Zbl 1279.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 30 2012 Reduced variational formulations in free boundary continuum mechanics. Zbl 1260.37031Gay-Balmaz, François; Marsden, Jerrold E.; Ratiu, Tudor S. 14 2012 Invariant higher-order variational problems. II. Zbl 1351.58009Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 14 2012 Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body. Zbl 1300.70005Birtea, Petre; Caşu, Ioan; Ratiu, Tudor S.; Turhan, Murat 11 2012 Dirac structures, nonholonomic systems and reduction. Zbl 1247.53096Jotz, Madeleine; Ratiu, T. S. 11 2012 Invariant frames for vector bundles and applications. Zbl 1319.70018Jotz, M.; Ratiu, T. S.; Zambon, M. 5 2012 Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution. Zbl 1266.58015Ratiu, T.; Filatova, T. A.; Shafarevich, A. I. 5 2012 Homogenization of the equations of dynamics of nematic liquid crystals with inhomogeneous density. Zbl 1264.82148Romanov, M. C.; Ratiu, T. S.; Chechkin, G. A. 4 2012 Euler-Poincaré approaches to nematodynamics. Zbl 1278.82062Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 3 2012 Exact geometric theory of dendronized polymer dynamics. Zbl 1257.82113Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 3 2012 Circle-valued momentum maps for symplectic periodic flows. Zbl 1269.53078Pelayo, Álvaro; Ratiu, Tudor S. 3 2012 The momentum map representation of images. Zbl 1211.58010Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 23 2011 Clebsch optimal control formulation in mechanics. Zbl 1233.49005Gay-Balmaz, François; Ratiu, Tudor S. 17 2011 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 17 2011 Lagrange-Poincaré field equations. Zbl 1253.70031Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 12 2011 Singular reduction of Dirac structures. Zbl 1385.70039Jotz, M.; Ratiu, T. S.; Śniatycki, J. 8 2011 Induced Dirac structures on isotropy-type manifolds. Zbl 1271.70033Jotz, M.; Ratiu, T. S. 4 2011 Geometry of nonabelian charged fluids. Zbl 1229.37098Gay-Balmaz, François; Ratiu, Tudor S. 4 2011 Coadjoint orbits and the beginnings of a geometric representation theory. Zbl 1223.22019Ratiu, Tudor S. 3 2011 Invariant generators for generalized distributions. Zbl 1273.70034Jotz, Madeleine; Ratiu, Tudor S. 1 2011 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 24 2010 A new Lagrangian dynamic reduction in field theory. Zbl 1404.58029Gay-Balmaz, François; Ratiu, Tudor S. 15 2010 The geometric structure of complex fluids. Zbl 1161.37052Gay-Balmaz, François; Ratiu, Tudor S. 36 2009 The momentum map in Poisson geometry. Zbl 1180.53083Fernandes, Rui Loja; Ortega, Juan-Pablo; Ratiu, Tudor S. 16 2009 Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 8 2009 A class of integrable flows on the space of symmetric matrices. Zbl 1231.37030Bloch, Anthony M.; Brînzănescu, Vasile; Iserles, Arieh; Marsden, Jerrold E.; Ratiu, Tudor S. 5 2009 Openness and convexity for momentum maps. Zbl 1163.53053Birtea, Petre; Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2009 Poisson reduction by distributions. Zbl 1204.53071Jotz, Madeleine; Ratiu, Tudor S. 2 2009 Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids. Zbl 1149.70015Gay-Balmaz, François; Ratiu, Tudor S. 9 2008 Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids. Zbl 1143.76061Gay-Balmaz, François; Ratiu, Tudor S. 4 2008 Induced and coinduced Banach Lie-Poisson spaces and integrability. Zbl 1157.53044Odzijewicz, Anatol; Ratiu, Tudor S. 4 2008 Induction for weak symplectic Banach manifolds. Zbl 1145.53061Odzijewicz, Anatol; Ratiu, Tudor S. 3 2008 A local-to-global principle for convexity in metric spaces. Zbl 1148.53030Birtea, Petre; Ortega, Juan-Pablo; Ratiu, Tudor S. 3 2008 Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations. Zbl 1151.37057Gay-Balmaz, François; Ratiu, Tudor S. 1 2008 Hamiltonian reduction by stages. Zbl 1129.37001Marsden, Jerrold E.; Misiołek, Gerard; Ortega, Juan-Pablo; Perlmutter, Matthew; Ratiu, Tudor S. 68 2007 The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits. Zbl 1120.22007Beltiţă, Daniel; Ratiu, Tudor S.; Tumpach, Alice Barbara 18 2007 Geometric representation theory for unitary groups of operator algebras. Zbl 1108.22008Beltiţă, Daniel; Ratiu, Tudor S. 8 2007 Group actions on chains of Banach manifolds and applications to fluid dynamics. Zbl 1122.58006Gay-Balmaz, François; Ratiu, Tudor S. 3 2007 The reduced spaces of a symplectic Lie group action. Zbl 1102.53059Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2006 The stratified spaces of a symplectic Lie group action. Zbl 1121.37040Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2006 On the symmetry breaking phenomenon. Zbl 1095.70008Birtea, Petre; Puta, Mircea; Ratiu, Tudor S.; Tudoran, Răzvan Micu 1 2006 A crash course in geometric mechanics. (Notes of the courses given by Tudor Ratiu). Zbl 1159.70001Ratiu, T. S.; Tudoran, R.; Sbano, L.; Sousa Dias, E.; Terra, G. 17 2005 Asymptotic and Lyapunov stability of constrained and Poisson equilibria. Zbl 1066.37017Ortega, Juan-Pablo; Planas-Bielsa, Víctor; Ratiu, Tudor S. 12 2005 Symplectic leaves in real Banach Lie-Poisson spaces. Zbl 1083.58011Beltiţă, D.; Ratiu, T. S. 8 2005 The Lie-Poisson structure of the LAE-\(\alpha\) equation. Zbl 1099.35096Gay-Balmaz, François; Ratiu, Tudor S. 4 2005 Geometric mechanics and symmetry; the Peyresq lectures. Lecture notes from the European Summer Schools in Geometric Mechanics held in Peyresq, 2000/2001. Zbl 1137.70001 2 2005 The universal covering and covered spaces of a symplectic Lie algebra action. Zbl 1079.53131Ortega, Juan-Pablo; Ratiu, Tudor S. 1 2005 Symmetry breaking for toral actions in simple mechanical systems. Zbl 1222.70023Birtea, Petre; Puta, Mircea; Ratiu, Tudor S.; Tudoran, Răzvan 1 2005 Momentum maps and Hamiltonian reduction. Zbl 1241.53069Ortega, Juan-Pablo; Ratiu, Tudor S. 124 2004 Singular reduction of implicit Hamiltonian systems. Zbl 1065.37040Blankenstein, Guido; Ratiu, Tudor S. 16 2004 Extensions of Banach Lie-Poisson spaces. Zbl 1067.53065Odzijewicz, Anatol; Ratiu, Tudor S. 6 2004 Controllability of Poisson systems. Zbl 1101.93008Birtea, Petre; Puta, Mircea; Ratiu, Tudor S. 3 2004 Cocycles, compatibility, and Poisson brackets for complex fluids. Zbl 1082.76011Cendra, Hernán; Marsden, Jerrold; Ratiu, Tudor S. 3 2004 Some remarks on a certain class of axisymmetric fluids of differential type. Zbl 1054.76006Busuioc, Adriana Valentina; Ratiu, Tudor S. 2 2004 Relative equilibria near stable and unstable Hamiltonian relative equilibria. Zbl 1068.37036Ortega, Juan-Pablo; Ratiu, Tudor S. 1 2004 The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. Zbl 1026.76004Busuioc, Adriana Valentina; Ratiu, Tudor S. 39 2003 Banach Lie-Poisson spaces and reduction. Zbl 1044.53057Odzijewicz, Anatol; Ratiu, Tudor S. 33 2003 ...and 96 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,719 Authors 88 Holm, Darryl D. 88 Ratiu, Tudor Stefan 67 Marsden, Jerrold Eldon 51 Gay-Balmaz, François 44 Bloch, Anthony Michael 23 Martín de Diego, David 20 Tudoran, Răzvan Micu 17 Guha, Partha 17 Leok, Melvin 17 Putkaradze, Vakhtang 17 Tronci, Cesare 16 Ortega, Juan-Pablo 15 García-Naranjo, Luis C. 15 Smolyanov, Oleg Georgievich 14 Beltiţă, Daniel 14 Colombo, Leonardo Jesus 14 Esen, Oğul 14 Marrero, Juan Carlos 13 Birtea, Petre 13 Modin, Klas 13 Pelayo, Alvaro 12 Mestdag, Tom 12 Montaldi, James A. 11 Chechkin, Gregory Aleksandrovich 11 Cotter, Colin John 11 Grmela, Miroslav 11 McLachlan, Robert I. 11 Simo, Juan Carlos 11 Vizman, Cornelia 11 Yoshimura, Hiroaki 11 Zenkov, Dmitry V. 10 Arnaudon, Alexis 10 Cendra, Hernán 10 de León Rodríguez, Manuel 10 Krishnaprasad, P.s. 10 Kupershmidt, Boris A. 10 Llibre, Jaume 10 Mardare, Cristinel 10 Miranda, Eva 10 Odzijewicz, Anatol 10 Shashikanth, Banavara N. 10 Svendsen, Bob 10 Vialard, François-Xavier 9 Andruchow, Esteban 9 Avendaño-Camacho, Misael 9 Castrillón López, Marco 9 Fehér, László Gy. 9 Gümral, Hasan 9 Jotz, Madeleine 9 Ohsawa, Tomoki 9 Pedroni, Marco 9 Rudolph, Gerd 9 Younes, Laurent 8 Adams, Malcolm R. 8 Bauer, Martin 8 Ciarlet, Philippe Gaston 8 Desbrun, Mathieu 8 Ferrer, Sebastián 8 Hernández-Bermejo, Benito 8 Leonard, Naomi Ehrich 8 Lewis, Debra 8 Patrick, George W. 8 Preston, Stephen C. 8 Shepherd, Theodore G. 8 Śniatycki, Jędrzej 8 Titi, Edriss Saleh 7 Balseiro, Paula 7 Biggs, Rory 7 Bruveris, Martins 7 Chiumiento, Eduardo 7 Dullin, Holger R. 7 Fassò, Francesco 7 Ibort, Alberto 7 Ivanov, Rossen I. 7 Kirillov, Oleg N. 7 Kolev, Boris 7 Lăzureanu, Cristian 7 Marmo, Giuseppe 7 Oliver, Marcel 7 Pelletier, Fernand 7 Perlmutter, Matthew 7 Pusztai, Béla Gábor 7 Puta, Mircea 7 Smolentsev, Nicolai Konstantinovich 7 Stoica, Cristina 7 Trouvé, Alain 7 Vankerschaver, Joris 7 Vera, Juan A. 7 Weinstein, Alan David 7 Yin, Zhaoyang 7 Zuccalli, Marcela 6 Barretta, Raffaele 6 Bogoyavlenskij, Oleg Igorevich 6 Bridges, Thomas J. 6 Busuioc, Adriana Valentina 6 Butscher, Adrian 6 Camassa, Roberto 6 Cantrijn, Frans 6 Caşu, Ioan 6 Comănescu, Dan ...and 2,619 more Authors all top 5 Cited in 394 Serials 137 Journal of Geometry and Physics 136 Journal of Mathematical Physics 108 Physica D 81 Journal of Nonlinear Science 67 Communications in Mathematical Physics 60 Journal of Differential Equations 59 Journal of Geometric Mechanics 48 International Journal of Geometric Methods in Modern Physics 43 Differential Geometry and its Applications 42 Journal of Mathematical Analysis and Applications 40 Letters in Mathematical Physics 39 Regular and Chaotic Dynamics 37 Reports on Mathematical Physics 34 Archive for Rational Mechanics and Analysis 33 Journal of Fluid Mechanics 33 Transactions of the American Mathematical Society 27 Acta Mechanica 27 Journal of Functional Analysis 27 Acta Applicandae Mathematicae 24 Physics of Fluids 23 Foundations of Computational Mathematics 22 Advances in Mathematics 22 Annals of Global Analysis and Geometry 21 Nonlinear Dynamics 20 Computer Methods in Applied Mechanics and Engineering 20 Systems & Control Letters 19 Theoretical and Mathematical Physics 18 Doklady Mathematics 17 Linear Algebra and its Applications 16 Journal of Computational Physics 16 Nonlinearity 16 Proceedings of the American Mathematical Society 15 Nonlinear Analysis. 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