Bernard Patrick - CV


Bernard Patrick

Professeur des universités

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Tel : 01 44 05 48 72

Bureau : C 618 bis



Suhr S., Bernard P. (2020), Cauchy and uniform temporal functions of globally hyperbolic cone fields, Proceedings of the American Mathematical Society

Bernard P., Suhr S. (2018), Smoothing causal functions, Journal of Physics. Conference Series, vol. 968, p. 7

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., 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

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., Labrousse C. (2016), An entropic characterization of the flat metrics on the two torus, Geometriae Dedicata, vol. 180, n°1, p. 187-201

Bernard P. (2016), Formes normales de champs de vecteurs, Gazette des Mathématiciens, n°148, p. 25-33

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. (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., 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. (2010), Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems, Annales Henri Poincaré, vol. 11, n°5, p. 929-942

Bernard P. (2010), On the Conley decomposition of Mather sets, Revista Matematica Iberoamericana, vol. 26, n°1, p. 115-132

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., 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

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), Young measures, superposition and transport, Indiana University Mathematics Journal, vol. 57, n°1, p. 247-276

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), The dynamics of pseudographs in convex Hamiltonian systems, Journal of the American Mathematical Society, vol. 21, n°3, p. 615-669

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), 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), 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), Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits, Journal of Differential Equations, vol. 180, n°2, p. 427-452

Bernard P. (2002), Connecting orbits of time dependent Lagrangian systems, Annales de l'Institut Fourier, vol. 52, n°5, p. 1533-1568

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), Arnold's Diffusion: from the a priori unstable to the a priori stable case., ICM 2010, Hyderabad, Inde

Bernard P. (2012), Some remarks on the continuity equation, Séminaire: Équations aux Dérivées Partielles, Palaiseau, France

Prépublications / Cahiers de recherche

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.

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