CEREMADE
Bernard Patrick
Full Professor
Publications
Articles
Bernard P. (2024), Non-degeneracy of closed orbits for generic potentials, Journal de l'école Polytechnique. Mathématiques, vol. 11, p. 363-393 
Bernard P. (2023), The Siegel-Bruno linearization Theorem, Regular and Chaotic Dynamics, vol. 28, n°4-5, p. 756-762
Aslani S., Bernard P. (2022), Normal form near orbit segments of convex Hamiltonian systems, International Mathematics Research Notices, vol. Volume 2022, n°11, p. 8196–8208
Suhr S., Bernard P. (2020), Cauchy and uniform temporal functions of globally hyperbolic cone fields, Proceedings of the American Mathematical Society, vol. 148, p. 4951-4966
Bernard P., Suhr S. (2018), Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions, Communications in Mathematical Physics, vol. 359, n°2, p. 467-498
Bernard P., Suhr S. (2018), Smoothing causal functions, Journal of Physics. Conference Series, vol. 968, p. 7
Bernard P., Kaloshin V., Zhang K. (2017), Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders, Acta Mathematica, vol. 217, n°1, p. 1-79
Bernard P. (2016), Formes normales de champs de vecteurs, Gazette des Mathématiciens, n°148, p. 25-33
Bernard P., Labrousse C. (2016), An entropic characterization of the flat metrics on the two torus, Geometriae Dedicata, vol. 180, n°1, p. 187-201
Jézéquel T., Bernard P., Lombardi E. (2016), Homoclinic orbits with many loops near a 02iω resonant fixed point of Hamiltonian systems, Discrete and Continuous Dynamical Systems, vol. 36, n°6, p. 3153-3225
Bernard P., Mandorino V. (2015), Some remarks on Thom's Transversality Theorem, Annali della Scuola Normale Superiore di Pisa, vol. 14, n°2, p. 361-386
Bernard P. (2013), Semi-concave singularities and the Hamilton-Jacobi equation, Regular and Chaotic Dynamics, vol. 18, n°6, p. 674-685
Bernard P., Zavidovique M. (2013), Regularization of subsolutions in discrete weak KAM theory, Canadian Journal of Mathematics, vol. 65, p. 740-756
Bernard P., Santos J. (2012), A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud., Mathematical Proceedings of the Cambridge Philosophical Society, vol. 152, n°1, p. 167-178
Bernard P. (2012), The Lax-Oleinik semi-group: a Hamiltonian point of view, Proceedings of the Royal Society of Edinburgh. Section A, Mathematical and Physical Sciences, vol. 142, n°6, p. 1131-1177
Bernard P. (2010), On the Number of Mather Measures of Lagrangian Systems, Archive for Rational Mechanics and Analysis, vol. 197, n°3, p. 1011-1031
Bernard P. (2010), Lasry-Lions regularization and a Lemma of Ilmanen, Rendiconti del Seminario Matematico della Università di Padova, vol. 124, p. 221-229
Bernard P. (2010), On the Conley decomposition of Mather sets, Revista Matematica Iberoamericana, vol. 26, n°1, p. 115-132
Bernard P., Bessi U. (2010), Young measures, Cartesian maps, and polyconvexity, Journal of the Korean Mathematical Society, vol. 47, n°2, p. 331-350
Bernard P., Santos J. (2010), A geometric definition of the Aubry-Mather set, Journal of Topology and Analysis, vol. 2, n°3, p. 385-393
Bernard P. (2010), Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems, Annales Henri Poincaré, vol. 11, n°5, p. 929-942
Ambrosio L., Bernard P. (2008), Uniqueness of signed measures solving the continuity equation for Osgood vector fields, Atti della Accademia Nazionale dei Lincei. Classe di scienze fisiche, matematiche e naturali, Matematica e applicazioni, vol. 19, n°3, p. 237--245
Bernard P. (2008), The dynamics of pseudographs in convex Hamiltonian systems, Journal of the American Mathematical Society, vol. 21, n°3, p. 615-669
Bernard P., Contreras G. (2008), A generic property of families of Lagrangian systems, Annals of Mathematics, vol. 167, n°3, p. 1099-1108
Bernard P. (2008), Young measures, superposition and transport, Indiana University Mathematics Journal, vol. 57, n°1, p. 247-276
Bernard P. (2007), Smooth critical sub-solutions of the Hamilton-Jacobi equation, Mathematical Research Letters, vol. 14, n°3, p. 503-511
Buffoni B., Bernard P. (2007), Optimal mass transportation and Mather theory, Journal of the European Mathematical Society, vol. 9, n°1, p. 85-121
Bernard P. (2007), Existence of C1,1 critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds, Annales scientifiques de l'Ecole normale supérieure, vol. 40, n°3, p. 445-452
Bernard P. (2007), Symplectic aspects of Mather theory, Duke Mathematical Journal, vol. 136, n°3, p. 401-420
Buffoni B., Bernard P. (2006), The Monge problem for supercritical Mane potentials on compact manifolds, Advances in Mathematics, vol. 207, n°2, p. 691-706
Bernard P. (2003), Homoclinic orbit to a center manifold, Calculus of Variations and Partial Differential Equations, vol. 17, n°2, p. 121-157
Bernard P. (2002), Connecting orbits of time dependent Lagrangian systems, Annales de l'Institut Fourier, vol. 52, n°5, p. 1533-1568
Bernard P. (2002), Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits, Journal of Differential Equations, vol. 180, n°2, p. 427-452
Bernard P. (2000), Homoclinic orbits to invariant sets of quasi-integrable exact maps, Ergodic Theory and Dynamical Systems, vol. 20, n°6, p. 1583-1601
Bernard P. (1996), Perturbation d'un hamiltonien partiellement hyperbolique, Comptes rendus. Mathématique, vol. 323, n°2, p. 189-194
Chapitres d'ouvrage
Bernard P. (2006), Hamiltonian Systems: Stability and Instability Theory, in Tsou, S.T., Encyclopedia of Mathematical Physics Elsevier, p. 261
Communications avec actes
Buffoni B., Bernard P. (2007), Weak KAM pairs and Monge-Kantorovich duality, in Yanagida, Eiji, Asymptotic Analysis and Singularities: Elliptic and Parabolic PDEs and Related Problems, Sendai, American Mathematical Society, 410 p.
Communications sans actes
Bernard P. (2012), Some remarks on the continuity equation, Séminaire: Équations aux Dérivées Partielles, Palaiseau, France
Bernard P. (2012), Arnold's Diffusion: from the a priori unstable to the a priori stable case., ICM 2010, Hyderabad, Inde
Prépublications / Cahiers de recherche
Aslani S., Bernard P. (2022), Bumpy metric theorem in the sense of Mané for non-convex Hamiltonians, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 18 p.
Bernard P., Suhr S. (2017), On causal functions, Paris, Cahier de recherche CEREMADE, Université Paris Dauphine-PSL, 7 p.
Jézéquel T., Bernard P., Lombardi E. (2014), Homoclinic connections with many loops near a 02iw resonant fixed point for Hamiltonian systems, Paris, Preprints Ceremade, 79 p.