Edit Profile (opens in new tab) Ratiu, Tudor Stefan Co-Author Distance Author ID: ratiu.tudor-stefan Published as: Ratiu, Tudor S.; Ratiu, Tudor; Ratiu, T. S.; Ratiu, T.; Ratiu, Tudor Stefan more...less 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: 257 Publications since 1972, including 16 Books and 20 Additional arXiv Preprints 16 Contributions as Editor Reviewing Activity: 83 Reviews Biographic References: 1 Publication Co-Authors: 142 Co-Authors with 258 Joint Publications 3,425 Co-Co-Authors all top 5 Co-Authors 13 single-authored 46 Marsden, Jerrold Eldon 33 Gay-Balmaz, François 27 Ortega, Juan-Pablo 22 Bloch, Anthony Michael 20 Holm, Darryl Dallas 12 Smolyanov, Oleg Georgievich 8 Birtea, Petre 8 Castrillón López, Marco 8 Flaschka, Hermann 8 Gough, John E. 8 Lewis, Debra 8 Pelayo, Alvaro 8 Schmid, Rudolf 8 Weinstein, Alan David 7 Jotz Lean, Madeleine 6 Cendra, Hernán 6 Chechkin, Gregory Aleksandrovich 6 Nguyen Tien Zung 6 Odzijewicz, Anatol 5 Adams, Malcolm R. 5 Demoures, François 5 Krishnaprasad, P.s. 5 Montgomery, Richard 5 Raugel, Geneviève 4 Bao, David 4 Diez, Tobias 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 Crouch, Peter E. 3 Derks, Gianne 3 Desbrun, Mathieu 3 Eliashberg, Yakov Matveevich 3 Newell, Alan C. 3 Perlmutter, Matthew 3 Romanov, Maksim S. 3 Samokhin, Vyacheslav N. 3 Scheurle, Jürgen 3 Vũ Ngọc, San 2 Abraham, Ralph Herman 2 Brînzănescu, Vasile 2 Craioveanu, Mircea-Eugen 2 Cruzeiro, Ana-Bela 2 Dobrogowska, Alina 2 Drăgulete, Oana M. 2 Ellis, David C. P. 2 Iserles, Arieh 2 Jiang, Kai 2 Martín de Diego, David 2 Mazer, Arthur A. 2 Meier, David M. 2 Michor, Peter Wolfram 2 Misiołek, Gerard 2 Montaldi, James 2 Muñoz Masqué, Jaime 2 Neeb, Karl-Hermann 2 Putkaradze, Vakhtang 2 Reghiş, Mircea 2 Rodríguez-Olmos, Miguel 2 Rozanova, Olga S. 2 Shafarevich, Andreĭ Igorevich 2 Shkoller, Steve 2 Simo, Juan Carlos 2 Tarama, Daisuke 2 Tumpach, Alice Barbara 2 Vialard, François-Xavier 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 Calini, Annalisa M. 1 Caşu, Ioan 1 Chang, Dong Eui 1 Chechkina, Tatiana P. 1 Chen, Xin 1 Chorin, Alexandre Joel 1 Dellnitz, Michael 1 Fassò, Francesco 1 Fernandes, Rui Loja 1 Filatova, T. A. 1 Futaki, Akito 1 García-Naranjo, Luis C. 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 ...and 50 more Co-Authors all top 5 Serials 11 Doklady Mathematics 10 Communications in Mathematical Physics 8 Nonlinearity 8 Physica D 7 Journal of Geometry and Physics 6 Letters in Mathematical Physics 6 Journal of Nonlinear Science 5 Transactions of the American Mathematical Society 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 Memoirs of the American Mathematical Society 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 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 Séminaire de Mathématiques Supérieures. Séminaire Scientifique OTAN (NATO Advanced Study Institute) 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 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 120 Dynamical systems and ergodic theory (37-XX) 100 Differential geometry (53-XX) 96 Mechanics of particles and systems (70-XX) 58 Global analysis, analysis on manifolds (58-XX) 45 Fluid mechanics (76-XX) 33 Partial differential equations (35-XX) 26 Topological groups, Lie groups (22-XX) 22 Nonassociative rings and algebras (17-XX) 16 General and overarching topics; collections (00-XX) 16 Quantum theory (81-XX) 15 Functional analysis (46-XX) 13 Mechanics of deformable solids (74-XX) 9 Ordinary differential equations (34-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Manifolds and cell complexes (57-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 History and biography (01-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Systems theory; control (93-XX) 5 Numerical analysis (65-XX) 4 Operator theory (47-XX) 3 Algebraic geometry (14-XX) 3 Probability theory and stochastic processes (60-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 2 Convex and discrete geometry (52-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 211 Publications have been cited 5,474 times in 3,504 Documents Cited by ▼ Year ▼ Introduction to mechanics and symmetry. A basic exposition of classical mechanical systems. 2nd ed. Zbl 0933.70003 Marsden, Jerrold E.; Ratiu, Tudor S. 655 1999 Manifolds, tensor analysis, and applications. 2nd ed. Zbl 0875.58002 Abraham, R.; Marsden, J. E.; Ratiu, T. 613 1988 The Euler-Poincaré equations and semidirect products with applications to continuum theories. Zbl 0951.37020 Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 384 1998 Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems. Zbl 0811.70002 Marsden, Jerrold E.; Ratiu, Tudor S. 310 1994 Nonlinear stability of fluid and plasma equilibria. Zbl 0717.76051 Holm, D. D.; Marsden, J. E.; Ratiu, T.; Weinstein, A. 285 1985 Momentum maps and Hamiltonian reduction. Zbl 1241.53069 Ortega, Juan-Pablo; Ratiu, Tudor S. 177 2004 Reduction of Poisson manifolds. Zbl 0602.58016 Marsden, Jerrold E.; Ratiu, Tudor 123 1986 Semidirect products and reduction in mechanics. Zbl 0529.58011 Marsden, Jerrold E.; Ratiu, Tudor; Weinstein, Alan 120 1984 Manifolds, tensor analysis, and applications. Zbl 0508.58001 Abraham, Ralph; Marsden, Jerrold E.; Ratiu, Tudor 119 1983 Hamiltonian reduction by stages. Zbl 1129.37001 Marsden, Jerrold E.; Misiołek, Gerard; Ortega, Juan-Pablo; Perlmutter, Matthew; Ratiu, Tudor S. 109 2007 Reduction, symmetry, and phases in mechanics. Zbl 0713.58052 Marsden, J. E.; Montgomery, R.; Ratiu, T. 97 1990 Lagrangian reduction by stages. Zbl 1193.37072 Cendra, Hernán; Marsden, Jerrold E.; Ratiu, Tudor S. 90 2001 The Euler-Poincaré equations and double bracket dissipation. Zbl 0846.58048 Bloch, Anthony; Krishnaprasad, P. S.; Marsden, Jerrold E.; Ratiu, Tudor S. 69 1996 Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\). Zbl 0643.35098 Flaschka, H.; Newell, A. C.; Ratiu, T. 60 1983 The Hamiltonian structure for dynamic free boundary problems. Zbl 0638.58044 Lewis, Debra; Marsden, J.; Montgomery, R.; Ratiu, T. 58 1986 The motion of the free \(n\)-dimensional rigid body. Zbl 0432.70011 Ratiu, Tudor 50 1980 The second-grade fluid and averaged Euler equations with Navier-slip boundary conditions. Zbl 1026.76004 Busuioc, Adriana Valentina; Ratiu, Tudor S. 46 2003 The geometric structure of complex fluids. Zbl 1161.37052 Gay-Balmaz, François; Ratiu, Tudor S. 46 2009 Reduction theory and the Lagrange-Routh equations. Zbl 1044.37043 Marsden, Jerrold E.; Ratiu, Tudor S.; Scheurle, Jürgen 46 2000 Completely integrable gradient flows. Zbl 0766.58027 Bloch, Anthony M.; Brockett, Roger W.; Ratiu, Tudor S. 45 1992 Dissipation induced instabilities. Zbl 0834.58025 Bloch, A. M.; Krishnaprasad, P. S.; Marsden, J. E.; Ratiu, T. S. 42 1994 Banach Lie-Poisson spaces and reduction. Zbl 1044.53057 Odzijewicz, Anatol; Ratiu, Tudor S. 42 2003 Invariant higher-order variational problems. Zbl 1279.58009 Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 39 2012 The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. Zbl 0979.58004 Marsden, J. E.; Ratiu, T. S.; Shkoller, S. 36 2000 Geometric mechanics, Lagrangian reduction, and nonholonomic systems. Zbl 1021.37001 Cendra, Hernán; Marsden, Jerrold E.; Ratiu, Tudor S. 36 2001 Reduction and Hamiltonian structures on duals of semidirect product Lie algebras. Zbl 0546.58025 Marsden, Jerrold E.; Ratiu, Tudor; Weinstein, Alan 35 1984 Hamiltonian systems with symmetry, coadjoint orbits and plasma physics. Zbl 0577.58013 Marsden, J. E.; Weinstein, A.; Ratiu, T.; Schmid, R.; Spencer, R. G. 35 1983 Variational principles for Lie-Poisson and Hamilton-Poincaré equations. Zbl 1156.37314 Cendra, Hernan; Marsden, Jerrold E.; Pekarsky, Sergey; Ratiu, Tudor S. 34 2003 Nonlinear stability analysis of stratified fluid equilibria. Zbl 0637.76119 Abarbanel, H. D. I.; Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 33 1986 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029 Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 33 2010 Euler-Poincaré reduction on principal bundles. Zbl 1020.58018 Castrillón López, M.; García Pérez, P. L.; Ratiu, T. S. 32 2001 Reduction in principal bundles: covariant Lagrange-Poincaré equations. Zbl 1037.53056 Castrillón López, M.; Ratiu, T. S. 32 2003 Gauged Lie-Poisson structures. Zbl 0546.58026 Montgomery, Richard; Marsden, Jerrold; Ratiu, Tudor 31 1984 Lagrangian reduction, the Euler-Poincaré equations, and semidirect products. Zbl 0989.37052 Cendra, Hernán; Holm, Darryl D.; Marsden, Jerrold E.; Ratiu, Tudor S. 30 1998 The Hamiltonian structure of continuum mechanics in material, inverse material, spatial and convective representations. Zbl 0611.70015 Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 30 1986 The momentum map representation of images. Zbl 1211.58010 Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 28 2011 Reduction in principal fiber bundles: Covariant Euler-Poincaré equations. Zbl 0967.53019 Castrillón López, Marco; Ratiu, Tudor S.; Shkoller, Steve 27 2000 Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body. Zbl 0509.58026 Ratiu, Tudor 27 1982 A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra. Zbl 0715.58004 Bloch, A. M.; Flaschka, H.; Ratiu, T. 27 1990 Stability of Hamiltonian relative equilibria. Zbl 0984.37063 Ortega, Juan-Pablo; Ratiu, Tudor S. 26 1999 The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits. Zbl 1120.22007 Beltiţă, Daniel; Ratiu, Tudor S.; Tumpach, Alice Barbara 26 2007 The differentiable structure of three remarkable diffeomorphism groups. Zbl 0451.58011 Ratiu, Tudor; Schmid, Rudolf 25 1981 The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation. Zbl 1320.32018 Gay-Balmaz, François; Ratiu, Tudor S. 24 2015 The heavy top: A geometric treatment. Zbl 0753.70004 Lewis, Debra; Ratiu, T.; Simo, J. C.; Marsden, J. E. 24 1992 Reduced variational formulations in free boundary continuum mechanics. Zbl 1260.37031 Gay-Balmaz, François; Marsden, Jerrold E.; Ratiu, Tudor S. 24 2012 The tropical momentum map: a classification of toric log symplectic manifolds. Zbl 1442.53057 Gualtieri, Marco; Li, Songhao; Pelayo, Álvaro; Ratiu, Tudor S. 24 2017 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 23 2011 Stability and bifurcation of a rotating planar liquid drop. Zbl 0651.76021 Lewis, Debra; Marsden, Jerrold Eldon; Ratiu, Tudor Stefan 22 1987 Invariant higher-order variational problems. II. Zbl 1351.58009 Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 22 2012 The momentum map in Poisson geometry. Zbl 1180.53083 Fernandes, Rui Loja; Ortega, Juan-Pablo; Ratiu, Tudor S. 22 2009 A crash course in geometric mechanics. (Notes of the courses given by Tudor Ratiu). Zbl 1159.70001 Ratiu, T. S.; Tudoran, R.; Sbano, L.; Sousa Dias, E.; Terra, G. 21 2005 Clebsch optimal control formulation in mechanics. Zbl 1233.49005 Gay-Balmaz, François; Ratiu, Tudor S. 20 2011 The C. Neumann problem as a completely integrable system on an adjoint orbit. Zbl 0475.58006 Ratiu, Tudor 20 1981 Lagrange-Poincaré field equations. Zbl 1253.70031 Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 20 2011 Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\). Zbl 1473.70029 Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S. 20 2014 A convexity theorem for Poisson actions of compact Lie groups. Zbl 0877.58025 Flaschka, Hermann; Ratiu, Tudor 20 1996 Discrete variational Lie group formulation of geometrically exact beam dynamics. Zbl 1315.53090 Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, S.; Ratiu, T. S.; Weinand, Y. 19 2015 A new Lagrangian dynamic reduction in field theory. Zbl 1404.58029 Gay-Balmaz, François; Ratiu, Tudor S. 19 2010 Symplectic connections and the linearisation of Hamiltonian systems. Zbl 0795.58018 Marsden, J. E.; Ratiu, T.; Raugel, G. 18 1991 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069 Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 17 2018 A new formulation of the generalized Toda lattice equations and their fixed point analysis via the momentum map. Zbl 0715.58033 Bloch, Anthony M.; Brockett, Roger W.; Ratiu, Tudor S. 17 1990 Singular reduction of implicit Hamiltonian systems. Zbl 1065.37040 Blankenstein, Guido; Ratiu, Tudor S. 17 2004 The Lagrange rigid body motion. Zbl 0466.58020 Ratiu, Tudor; van Moerbeke, P. 17 1982 The affine invariant of proper semitoric integrable systems. Zbl 1392.37046 Pelayo, Álvaro; Ratiu, Tudor S.; Ngọc, San Vu 17 2017 Singular reduction of Poisson manifolds. Zbl 0989.37070 Ortega, Juan-Pablo; Ratiu, Tudor S. 16 1998 Rotating \(n\)-gon/\(kn\)-gon vortex configurations. Zbl 0869.76012 Lewis, Debra; Ratiu, T. 16 1996 Nonlinear stability of singular relative periodic orbits in Hamiltonian systems with symmetry. Zbl 0955.37032 Ortega, Juan-Pablo; Ratiu, Tudor S. 15 1999 Symplectic reduction for semidirect products and central extensions. Zbl 0973.53069 Marsden, Jerrold E.; Misiołek, Gerard; Perlmutter, Matthew; Ratiu, Tudor S. 14 1998 A symplectic slice theorem. Zbl 1072.53541 Ortega, Juan-Pablo; Ratiu, Tudor S. 14 2002 On the nonlinear convexity theorem of Kostant. Zbl 0785.22019 Lu, Jiang-Hua; Ratiu, Tudor 14 1991 The diameter of the symplectomorphism group is infinite. Zbl 0725.58006 Eliashberg, Yakov; Ratiu, Tudor 14 1991 Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body. Zbl 0459.70007 Ratiu, Tudor 14 1981 Asymptotic and Lyapunov stability of constrained and Poisson equilibria. Zbl 1066.37017 Ortega, Juan-Pablo; Planas-Bielsa, Víctor; Ratiu, Tudor S. 13 2005 A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus. Zbl 0806.22012 Bloch, A. M.; Flaschka, H.; Ratiu, T. 12 1993 Nematodynamics and random homogenization. Zbl 1349.76017 Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S.; Romanov, Maksim S. 12 2016 Symplectic leaves in real Banach Lie-Poisson spaces. Zbl 1083.58011 Beltiţă, D.; Ratiu, T. S. 12 2005 On the geometry of the Virasoro-Bott group. Zbl 0945.58005 Michor, P. W.; Ratiu, T. S. 12 1998 Kac-Moody Lie algebras and soliton equations. III: Stationary equations associated with \(A_ 1^{(1)}\). Zbl 0643.35099 Flaschka, H.; Newell, A. C.; Ratiu, T. 12 1983 A Lie group structure for pseudodifferential operators. Zbl 0587.58047 Adams, Malcolm; Ratiu, Tudor; Schmid, Rudolf 12 1986 Singular reduction of Dirac structures. Zbl 1385.70039 Jotz, M.; Ratiu, T. S.; Śniatycki, J. 12 2011 Involution theorems. Zbl 0435.58014 Ratiu, Tudor 12 1980 Dirac structures, nonholonomic systems and reduction. Zbl 1247.53096 Jotz, Madeleine; Ratiu, T. S. 12 2012 Multisymplectic variational integrators and space/time symplecticity. Zbl 1338.65271 Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 12 2016 Stability of rigid body motion using the energy-Casimir method. Zbl 0526.70025 Holm, Darryl; Marsden, Jerrold; Ratiu, Tudor; Weinstein, Alan 11 1984 Hamiltonian structure and Lyapunov stability for ideal continuum dynamics. (Mathematical Seminar held at the University of Montréal, Canada, July 29 - August 16, 1985). Zbl 0594.00020 Holm, D. D.; Marsden, J. E.; Ratiu, T. S. 11 1986 Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids. Zbl 1149.70015 Gay-Balmaz, François; Ratiu, Tudor S. 11 2008 Equivalent theories of liquid crystal dynamics. Zbl 1361.76005 Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 11 2013 Geometric representation theory for unitary groups of operator algebras. Zbl 1108.22008 Beltiţă, Daniel; Ratiu, Tudor S. 11 2007 Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body. Zbl 1300.70005 Birtea, Petre; Caşu, Ioan; Ratiu, Tudor S.; Turhan, Murat 11 2012 The breadth of symplectic and Poisson geometry. Festschrift in honor of Alan Weinstein. Zbl 1062.53002 10 2005 The Lie group structure of diffeomorphism groups and invertible Fourier integral operators, with applications. Zbl 0617.58004 Adams, Malcolm; Ratiu, Tudor; Schmid, Rudolf 10 1985 The optimal momentum map. Zbl 1015.53053 Ortega, Juan-Pablo; Ratiu, Tudor S. 9 2002 Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems. Zbl 1321.37054 Bloch, Anthony M.; Morrison, Philip J.; Ratiu, Tudor S. 9 2013 Fiber connectivity and bifurcation diagrams of almost toric integrable systems. Zbl 1335.37042 Pelayo, Álvaro; Ratiu, Tudor S.; San Vũ Ngọc 9 2015 The symmetric representation of the rigid body equations and their discretization. Zbl 1064.70004 Bloch, Anthony M.; Crouch, Peter E.; Marsden, Jerrold E.; Ratiu, Tudor S. 9 2002 Geometric dynamics of optimization. Zbl 1271.49003 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 9 2013 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143 Ratiu, T. S.; Smolyanov, O. G. 9 2013 A Lie group structure for Fourier integral operators. Zbl 0619.58010 Adams, Malcolm; Ratiu, Tudor; Schmid, Rudolf 9 1986 Moduli spaces of toric manifolds. Zbl 1298.53088 Pelayo, Á.; Pires, A. R.; Ratiu, T. S.; Sabatini, S. 9 2014 Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 9 2009 Stochastic variational principles for dissipative equations with advected quantities. Zbl 1524.76329 Chen, Xin; Cruzeiro, Ana Bela; Ratiu, Tudor S. 6 2023 Convexity of singular affine structures and toric-focus integrable Hamiltonian systems. Zbl 1526.37002 Ratiu, Tudor S.; Wacheux, Christophe; Zung, Nguyen Tien 2 2023 Integrable systems in planar robotics. Zbl 1462.37068 Ratiu, Tudor Stefan; Zung, Nguyen Tien 1 2020 Quantum anomalies via differential properties of Lebesgue-Feynman generalized measures. Zbl 1453.81031 Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G. 1 2020 Geodesic flows on real forms of complex semi-simple Lie groups of rigid body type. Zbl 1460.53074 Ratiu, Tudor S.; Tarama, Daisuke 1 2020 Presymplectic convexity and (ir)rational polytopes. Zbl 1462.53067 Ratiu, Tudor; Nguyen, Tien Zung 8 2019 Preface. Zbl 1490.00063 1 2019 Momentum maps and stochastic Clebsch action principles. Zbl 1433.60069 Cruzeiro, Ana Bela; Holm, Darryl D.; Ratiu, Tudor S. 17 2018 The tropical momentum map: a classification of toric log symplectic manifolds. Zbl 1442.53057 Gualtieri, Marco; Li, Songhao; Pelayo, Álvaro; Ratiu, Tudor S. 24 2017 The affine invariant of proper semitoric integrable systems. Zbl 1392.37046 Pelayo, Álvaro; Ratiu, Tudor S.; Ngọc, San Vu 17 2017 The geometric nature of the Flaschka transformation. Zbl 1368.37065 Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S. 4 2017 A multisymplectic integrator for elastodynamic frictionless impact problems. Zbl 1439.74234 Demoures, François; Gay-Balmaz, François; Desbrun, Mathieu; Ratiu, Tudor S.; Aragón, Alejandro M. 3 2017 Noether theorems and quantum anomalies. Zbl 1366.81260 Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 2 2017 Existence and uniqueness theorems for the full three-dimensional Ericksen-Leslie system. Zbl 1362.76004 Chechkin, Gregory A.; Ratiu, Tudor S.; Romanov, Maxim S.; Samokhin, Vyacheslav N. 2 2017 Coadjoint orbits in duals of Lie algebras with admissible ideals. Zbl 1402.53064 Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S. 1 2017 Nematodynamics and random homogenization. Zbl 1349.76017 Chechkin, Gregory A.; Chechkina, Tatiana P.; Ratiu, Tudor S.; Romanov, Maksim S. 12 2016 Multisymplectic variational integrators and space/time symplecticity. Zbl 1338.65271 Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 12 2016 Multisymplectic variational integrators for nonsmooth Lagrangian continuum mechanics. Zbl 1416.65512 Demoures, François; Gay-Balmaz, François; Ratiu, Tudor S. 7 2016 Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties. Zbl 1420.17026 Hounkonnou, Mahouton Norbert; Guha, Partha; Ratiu, Tudor 6 2016 Existence and uniqueness theorems for the two-dimensional Ericksen-Leslie system. Zbl 1346.76010 Chechkin, Gregory A.; Ratiu, Tudor S.; Romanov, Maxim S.; Samokhin, Vyacheslav N. 4 2016 The geometry of the universal Teichmüller space and the Euler-Weil-Petersson equation. Zbl 1320.32018 Gay-Balmaz, François; Ratiu, Tudor S. 24 2015 Discrete variational Lie group formulation of geometrically exact beam dynamics. Zbl 1315.53090 Demoures, F.; Gay-Balmaz, F.; Leyendecker, S.; Ober-Blöbaum, S.; Ratiu, T. S.; Weinand, Y. 19 2015 Fiber connectivity and bifurcation diagrams of almost toric integrable systems. Zbl 1335.37042 Pelayo, Álvaro; Ratiu, Tudor S.; San Vũ Ngọc 9 2015 Geometry of non-holonomic diffusion. Zbl 1317.37064 Hochgerner, Simon; Ratiu, Tudor S. 8 2015 Quantum anomalies and logarithmic derivatives of Feynman pseudomeasures. Zbl 1341.81038 Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 5 2015 Noether’s theorem for dissipative quantum dynamical semi-groups. Zbl 1311.81161 Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G. 4 2015 Bi-Jacobi fields and Riemannian cubics for left-invariant \(\mathrm{SO}(3)\). Zbl 1330.70063 Noakes, Lyle; Ratiu, Tudor S. 4 2015 Wigner measures and quantum control. Zbl 1321.81030 Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 3 2015 Existence and uniqueness theorems in two-dimensional nematodynamics. Finite speed of propagation. Zbl 1330.82055 Ratiu, T. S.; Romanov, M. S.; Samokhin, V. N.; Chechkin, G. A. 3 2015 Lagrangian reductions and integrable systems in condensed matter. Zbl 1311.53067 Gay-Balmaz, François; Monastyrsky, Michael; Ratiu, Tudor S. 3 2015 The \(U(n)\) free rigid body: integrability and stability analysis of the equilibria. Zbl 1378.70005 Ratiu, Tudor S.; Tarama, Daisuke 2 2015 \(L^2\)-cohomology and complete Hamiltonian manifolds. Zbl 1304.53086 Mazzeo, Rafe; Pelayo, Álvaro; Ratiu, Tudor S. 1 2015 Hamiltonian structures in the quantum theory of Hamilton-Dirac systems. Zbl 1337.81086 Ratiu, T. S.; Smolyanov, O. G. 1 2015 Wigner quantization of Hamilton-Dirac systems. Zbl 1337.81082 Ratiu, T. S.; Smolyanov, O. G. 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 Integrable systems of Neumann type. Zbl 1338.37071 Dobrogowska, Alina; Ratiu, Tudor S. 1 2015 Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\). Zbl 1473.70029 Demoures, François; Gay-Balmaz, François; Kobilarov, Marin; Ratiu, Tudor S. 20 2014 Moduli spaces of toric manifolds. Zbl 1298.53088 Pelayo, Á.; Pires, A. R.; Ratiu, T. S.; Sabatini, S. 9 2014 Feynman, Wigner, and Hamiltonian structures describing the dynamics of open quantum systems. Zbl 1295.81097 Gough, J.; Ratiu, T. S.; Smolyanov, O. G. 8 2014 Integrable \(G\)-strands on semisimple Lie groups. Zbl 1298.22012 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 1 2014 Equivalent theories of liquid crystal dynamics. Zbl 1361.76005 Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 11 2013 Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems. Zbl 1321.37054 Bloch, Anthony M.; Morrison, Philip J.; Ratiu, Tudor S. 9 2013 Geometric dynamics of optimization. Zbl 1271.49003 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 9 2013 Hamiltonian and Feynman aspects of secondary quantization. Zbl 1312.81143 Ratiu, T. S.; Smolyanov, O. G. 9 2013 Thin layer of a non-Newtonian fluid flowing on a rough surface and percolating through a perforated obstacle. Zbl 1268.76003 Linkevich, A. Yu.; Ratiu, T. S.; Spiridonov, S. V.; Chechkin, G. A. 7 2013 Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold. Zbl 1292.81063 Ratiu, T. S.; Suleimanova, A. A.; Shafarevich, A. I. 7 2013 Dirac optimal reduction. Zbl 1275.37028 Jotz, M. M.; Ratiu, T. S. 4 2013 Extensions of Lie-Rinehart algebras and cotangent bundle reduction. Zbl 1304.53083 Huebschmann, J.; Perlmutter, M.; Ratiu, T. S. 2 2013 On the coupling between an ideal fluid and immersed particles. Zbl 1302.76007 Jacobs, 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 1279.58009 Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 39 2012 Reduced variational formulations in free boundary continuum mechanics. Zbl 1260.37031 Gay-Balmaz, François; Marsden, Jerrold E.; Ratiu, Tudor S. 24 2012 Invariant higher-order variational problems. II. Zbl 1351.58009 Gay-Balmaz, François; Holm, Darryl D.; Meier, David M.; Ratiu, Tudor S.; Vialard, François-Xavier 22 2012 Dirac structures, nonholonomic systems and reduction. Zbl 1247.53096 Jotz, Madeleine; Ratiu, T. S. 12 2012 Stability of equilibria for the \(\mathfrak{so}(4)\) free rigid body. Zbl 1300.70005 Birtea, Petre; Caşu, Ioan; Ratiu, Tudor S.; Turhan, Murat 11 2012 Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution. Zbl 1266.58015 Ratiu, T.; Filatova, T. A.; Shafarevich, A. I. 7 2012 Euler-Poincaré approaches to nematodynamics. Zbl 1278.82062 Gay-Balmaz, François; Ratiu, Tudor S.; Tronci, Cesare 5 2012 Exact geometric theory of dendronized polymer dynamics. Zbl 1257.82113 Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 5 2012 Invariant frames for vector bundles and applications. Zbl 1319.70018 Jotz, M.; Ratiu, T. S.; Zambon, M. 5 2012 Homogenization of the equations of dynamics of nematic liquid crystals with inhomogeneous density. Zbl 1264.82148 Romanov, M. C.; Ratiu, T. S.; Chechkin, G. A. 4 2012 Circle-valued momentum maps for symplectic periodic flows. Zbl 1269.53078 Pelayo, Álvaro; Ratiu, Tudor S. 4 2012 The momentum map representation of images. Zbl 1211.58010 Bruveris, M.; Gay-Balmaz, F.; Holm, D. D.; Ratiu, T. S. 28 2011 Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions. Zbl 1319.70022 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 23 2011 Clebsch optimal control formulation in mechanics. Zbl 1233.49005 Gay-Balmaz, François; Ratiu, Tudor S. 20 2011 Lagrange-Poincaré field equations. Zbl 1253.70031 Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 20 2011 Singular reduction of Dirac structures. Zbl 1385.70039 Jotz, M.; Ratiu, T. S.; Śniatycki, J. 12 2011 Geometry of nonabelian charged fluids. Zbl 1229.37098 Gay-Balmaz, François; Ratiu, Tudor S. 5 2011 Induced Dirac structures on isotropy-type manifolds. Zbl 1271.70033 Jotz, M.; Ratiu, T. S. 4 2011 Coadjoint orbits and the beginnings of a geometric representation theory. Zbl 1223.22019 Ratiu, Tudor S. 4 2011 Lectures on Poisson geometry. Based on a summer school, Trieste, Italy, July 4–22, 2005. Zbl 1214.53009 1 2011 Invariant generators for generalized distributions. Zbl 1273.70034 Jotz, Madeleine; Ratiu, Tudor S. 1 2011 Symmetry reduced dynamics of charged molecular strands. Zbl 1333.70029 Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Putkaradze, Vakhtang; Ratiu, Tudor S. 33 2010 A new Lagrangian dynamic reduction in field theory. Zbl 1404.58029 Gay-Balmaz, François; Ratiu, Tudor S. 19 2010 The geometric structure of complex fluids. Zbl 1161.37052 Gay-Balmaz, François; Ratiu, Tudor S. 46 2009 The momentum map in Poisson geometry. Zbl 1180.53083 Fernandes, Rui Loja; Ortega, Juan-Pablo; Ratiu, Tudor S. 22 2009 Variational principles for spin systems and the Kirchhoff rod. Zbl 1288.70012 Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S. 9 2009 Openness and convexity for momentum maps. Zbl 1163.53053 Birtea, Petre; Ortega, Juan-Pablo; Ratiu, Tudor S. 7 2009 A class of integrable flows on the space of symmetric matrices. Zbl 1231.37030 Bloch, Anthony M.; Brînzănescu, Vasile; Iserles, Arieh; Marsden, Jerrold E.; Ratiu, Tudor S. 6 2009 Poisson reduction by distributions. Zbl 1204.53071 Jotz, Madeleine; Ratiu, Tudor S. 2 2009 Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids. Zbl 1149.70015 Gay-Balmaz, François; Ratiu, Tudor S. 11 2008 A local-to-global principle for convexity in metric spaces. Zbl 1148.53030 Birtea, Petre; Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2008 Affine Lie-Poisson reduction, Yang-Mills magnetohydrodynamics, and superfluids. Zbl 1143.76061 Gay-Balmaz, François; Ratiu, Tudor S. 5 2008 Induced and coinduced Banach Lie-Poisson spaces and integrability. Zbl 1157.53044 Odzijewicz, Anatol; Ratiu, Tudor S. 5 2008 Induction for weak symplectic Banach manifolds. Zbl 1145.53061 Odzijewicz, Anatol; Ratiu, Tudor S. 4 2008 Poisson reduction and the Hamiltonian structure of the Euler-Yang-Mills equations. Zbl 1151.37057 Gay-Balmaz, François; Ratiu, Tudor S. 1 2008 Hamiltonian reduction by stages. Zbl 1129.37001 Marsden, Jerrold E.; Misiołek, Gerard; Ortega, Juan-Pablo; Perlmutter, Matthew; Ratiu, Tudor S. 109 2007 The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits. Zbl 1120.22007 Beltiţă, Daniel; Ratiu, Tudor S.; Tumpach, Alice Barbara 26 2007 Geometric representation theory for unitary groups of operator algebras. Zbl 1108.22008 Beltiţă, Daniel; Ratiu, Tudor S. 11 2007 Group actions on chains of Banach manifolds and applications to fluid dynamics. Zbl 1122.58006 Gay-Balmaz, François; Ratiu, Tudor S. 3 2007 Singular cosphere bundle reduction. Zbl 1128.53056 Drăgulete, Oana M.; Ratiu, Tudor S.; Rodríguez-Olmos, Miguel 1 2007 The stratified spaces of a symplectic Lie group action. Zbl 1121.37040 Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2006 The reduced spaces of a symplectic Lie group action. Zbl 1102.53059 Ortega, Juan-Pablo; Ratiu, Tudor S. 5 2006 On the symmetry breaking phenomenon. Zbl 1095.70008 Birtea, 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 1159.70001 Ratiu, T. S.; Tudoran, R.; Sbano, L.; Sousa Dias, E.; Terra, G. 21 2005 Asymptotic and Lyapunov stability of constrained and Poisson equilibria. Zbl 1066.37017 Ortega, Juan-Pablo; Planas-Bielsa, Víctor; Ratiu, Tudor S. 13 2005 Symplectic leaves in real Banach Lie-Poisson spaces. Zbl 1083.58011 Beltiţă, D.; Ratiu, T. S. 12 2005 The breadth of symplectic and Poisson geometry. Festschrift in honor of Alan Weinstein. Zbl 1062.53002 10 2005 The Lie-Poisson structure of the LAE-\(\alpha\) equation. Zbl 1099.35096 Gay-Balmaz, François; Ratiu, Tudor S. 5 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 4 2005 The universal covering and covered spaces of a symplectic Lie algebra action. Zbl 1079.53131 Ortega, Juan-Pablo; Ratiu, Tudor S. 1 2005 ...and 111 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,689 Authors 104 Holm, Darryl Dallas 100 Ratiu, Tudor Stefan 75 Marsden, Jerrold Eldon 68 Gay-Balmaz, François 48 Bloch, Anthony Michael 27 Esen, Oğul 27 Martín de Diego, David 26 Tronci, Cesare 22 Leok, Melvin 22 Tudoran, Răzvan Micu 20 García-Naranjo, Luis C. 20 Guha, Partha 20 Marrero Gonzalez, Juan Carlos 20 Putkaradze, Vakhtang 19 Colombo, Leonardo Jesus 19 de León Rodríguez, Manuel 18 Ortega, Juan-Pablo 17 Castrillón López, Marco 17 Grmela, Miroslav 17 Modin, Klas 17 Ohsawa, Tomoki 16 Miranda, Eva 16 Pelayo, Alvaro 16 Smolyanov, Oleg Georgievich 15 Beltiţă, Daniel 15 Birtea, Petre 14 Cotter, Colin John 14 Fehér, László Gy. 14 Gümral, Hasan 14 Mestdag, Tom 14 Vizman, Cornelia 14 Vorob’ev, Yu. M. 13 Chechkin, Gregory Aleksandrovich 13 Hernández-Bermejo, Benito 13 Krishnaprasad, P.s. 13 McLachlan, Robert I. 13 Montaldi, James 13 Yoshimura, Hiroaki 12 Arnaudon, Alexis 12 Cendra, Hernán 12 Grillo, Sergio Daniel 12 Marmo, Giuseppe 12 Ober-Blöbaum, Sina 12 Pavelka, Michal 12 Pedroni, Marco 12 Simo, Juan Carlos 12 Zenkov, Dmitry V. 11 de Lucas, Javier 11 Ferrer, Sebastián 11 Kirillov, Oleg N. 11 Mardare, Cristinel 11 Odzijewicz, Anatol 11 Shashikanth, Banavara N. 11 Śniatycki, Jędrzej 11 Svendsen, Bob 11 Zuccalli, Marcela 10 Avendaño-Camacho, Misael 10 Bauer, Martin 10 Ciarlet, Philippe Gaston 10 Crespo, Francisco 10 Desbrun, Mathieu 10 Kupershmidt, Boris A. 10 Lăzureanu, Cristian 10 Leonard, Naomi Ehrich 10 Leyendecker, Sigrid 10 Llibre, Jaume 10 Morrison, Philip J. 10 Preston, Stephen C. 10 Rudolph, Gerd 10 Vialard, François-Xavier 9 Andruchow, Esteban 9 Balseiro, Paula 9 Barretta, Raffaele 9 Betsch, Peter 9 Bogoyavlenskij, Oleg Igorevich 9 Cipriano, Fernanda 9 Comănescu, Dan 9 Crisan, Dan O. 9 Dullin, Holger R. 9 Falqui, Gregorio 9 Fassò, Francesco 9 Grabowski, Janusz 9 Ibort, Alberto 9 Jotz Lean, Madeleine 9 Kolev, Boris 9 Morosi, Carlo 9 Oliver, Marcel 9 Owren, Brynjulf 9 Puta, Mircea 9 Romano, Giovanni P. 9 Titi, Edriss Saleh 9 Younes, Laurent 8 Adams, Malcolm R. 8 Banavar, Ravi N. 8 Bullo, Francesco 8 Celledoni, Elena 8 Chiumiento, Eduardo 8 García-Toraño Andrés, Eduardo 8 Helmke, Uwe R. 8 Ivanov, Rossen I. ...and 3,589 more Authors all top 5 Cited in 467 Serials 181 Journal of Geometry and Physics 153 Journal of Mathematical Physics 148 Physica D 103 Journal of Nonlinear Science 76 Journal of Geometric Mechanics 71 Communications in Mathematical Physics 70 Journal of Differential Equations 64 Reports on Mathematical Physics 61 International Journal of Geometric Methods in Modern Physics 59 Physics Letters. 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