Nombre de documents


Patrick Bernard, Publications

Pré-publication, Document de travail2 documents

  • Patrick Bernard, Stefan Suhr. On causal functions. 2017. 〈hal-01633180〉
  • Patrick Bernard, Stefan Suhr. Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions.. 2017. 〈hal-01487859v2〉

Article dans une revue35 documents

  • Patrick Bernard, K Kaloshin, K Zhang. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica, Royal Swedish Academy of Sciences, Institut Mittag-Leffler, 2017, 217 (1), pp.1-79. 〈10.1007/s11511-016-0141-5〉. 〈hal-01435608〉
  • Patrick Bernard. Formes normales de champs de vecteurs . Gazette des Mathématiciens, Société Mathématique de France, 2016. 〈hal-01435605〉
  • Patrick Bernard, Clémence Labrousse. An entropic characterization of the flat metrics on the two torus. Geometriae Dedicata, Springer Verlag, 2016, 180 (1), pp.187 - 201. 〈10.1007/s10711-015-0098-0〉. 〈hal-00999563v2〉
  • Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2016, 36 (6), pp.3153-3225. 〈10.3934/dcds.2016.36.xx〉. 〈hal-01251087〉
  • Patrick Bernard, Vito Mandorino. Some remarks on Thom's Transversality Theorem. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2015, XIV (2), pp.631-386. 〈10.2422/2036-2145.201205_007〉. 〈hal-00713024v2〉
  • Patrick Bernard. Semi-concave singularities and the Hamilton-Jacobi equation. Regular and Chaotic Dynamics, MAIK Nauka/Interperiodica, 2013, 18 (6), pp.674-685. 〈10.1134/S1560354713060075〉. 〈hal-00999547〉
  • Patrick Bernard, Maxime Zavidovique. Regularization of Subsolutions in Discrete Weak KAM Theory. Canadian Journal of Mathematics, University of Toronto Press, 2013, 65, pp.740-756. 〈10.4153/CJM-2012-059-3〉. 〈hal-00678699v3〉
  • Patrick Bernard. The Lax–Oleinik semi-group: a Hamiltonian point of view. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 2012, 142 (6), pp.1131-1177. 〈10.1017/S0308210511000059〉. 〈hal-00678990v2〉
  • Patrick Bernard, Joana Santos. A geometric definition of the Mãné-Mather set and a Theorem of Marie-Claude Arnaud. Mathematical Proceedings, Cambridge University Press (CUP), 2012, 152 (1), pp.167-178. 〈10.1017/S0305004111000685〉. 〈hal-00678709v3〉
  • Patrick Bernard. On the Conley decomposition of Mather sets. Revista Matemática Iberoamericana, European Mathematical Society, 2010, 26 (1), pp.115-132. 〈10.4171/RMI/596〉. 〈hal-00294640v3〉
  • Patrick Bernard, Joana Santos. A geometric definition of the Aubry-Mather set. Journal of Topology and Analysis, 2010, 2 (3), pp.385-393. 〈10.1142/S1793525310000343〉. 〈hal-00678691〉
  • Patrick Bernard. Large Normally Hyperbolic Cylinders in a priori Stable Hamiltonian Systems. Annales de l'Institut Henri Poincaré, 2010, 11 (5), pp.929-942. 〈10.1007/s00023-010-0040-9〉. 〈hal-00438208v3〉
  • Patrick Bernard. Lasry-Lions Regularization and a Lemma of Ilmanen. Rendiconti del Seminario Matematico della Università di Padova, 2010, 124, pp.221-229. 〈10.4171/RSMUP/124-15〉. 〈hal-00448255v2〉
  • Patrick Bernard. On the number of Mather measures of Lagrangian systems. Archive for Rational Mechanics and Analysis, Springer Verlag, 2010, 197 (3), pp.1011-1031. 〈10.1007/s00205-009-0289-7〉. 〈hal-00448263v2〉
  • Patrick Bernard, Ugo Bessi. Young measures, Cartesian maps, and polyconvexity. Journal of the Korean Mathematical Society, The Korean Mathematical Society, 2010, 47 (2), pp.331-350. 〈10.4134/JKMS.2010.47.2.331〉. 〈hal-00294644v2〉
  • Luigi Ambrosio, Patrick Bernard. Uniqueness of signed measures solving the continuity equation for Osgood vector fields. Rendiconti Lincei - Matematica E Applicationi, 2008, 19 (3), pp.237--245. 〈10.4171/RLM/522〉. 〈hal-00294648〉
  • Patrick Bernard. The dynamics of pseudographs in convex Hamiltonian systems. Journal of the American Mathematical Society, American Mathematical Society, 2008, 21 (3), pp.615-669. 〈10.1090/S0894-0347-08-00591-2〉. 〈hal-00003588v2〉
  • Patrick Bernard. Young measure, superposition and transport. Indiana University Mathematics Journal, Indiana University Mathematics Journal, 2008, 57 (1), pp.247-276. 〈10.1512/iumj.2008.57.3163〉. 〈hal-00124907v3〉
  • Patrick Bernard, Gonzalo Contreras. A generic property of families of Lagrangian systems. Annals of Mathematics, Princeton University, Department of Mathematics, 2008, 167 (3), pp.1-10. 〈10.4007/annals.2008.167.1099〉. 〈hal-00294671〉
  • Patrick Bernard. Symplectic aspects of Aubry-Mather theory. Duke Mathematical Journal, Duke University Press, 2007, 136 (3), pp.401-420. 〈10.1215/S0012-7094-07-13631-7〉. 〈hal-00005069〉
  • Patrick Bernard, Boris Buffoni. Weak KAM pairs and Monge-Kantorovich duality. Advanced Studies in Pure Mathematics., 2007, Asymptotic analysis and singularities : elliptic and parabolic PDEs and related problems, 47 (2), pp.397-420. 〈hal-00014963v2〉
  • Patrick Bernard. Smooth critical sub-solutions of the Hamilton-Jacobi equation. Mathematical Research Letters, 2007, 14 (3), pp.503 - 511. 〈10.4310/MRL.2007.v14.n3.a14〉. 〈hal-00014966v2〉
  • Patrick Bernard, Boris Buffoni. Optimal mass transportation and Mather theory. Journal of the European Mathematical Society, European Mathematical Society, 2007, 9, pp.85-121. 〈10.4171/JEMS/74〉. 〈hal-00003587v3〉
  • Patrick Bernard. Existence of $C^{1,1}$ critical sub-solutions of the Hamilton-Jacobi equation on compact manifolds. Annales Scientifiques de l'École Normale Supérieure, Elsevier Masson, 2007, 40 (3), pp.445-452. 〈hal-00014965v4〉
  • Patrick Bernard, Boris Buffoni. The Monge problem for supercritical Mane potentials on compact manifolds. Advances in Mathematics, Elsevier, 2006, 207, pp.691-706. 〈10.1016/j.aim.2006.01.003〉. 〈hal-00004172v2〉
  • Patrick Bernard, Jean-Michel Roquejoffre. Convergence to Time-Periodic Solutions in Time-Periodic Hamilton–Jacobi Equations on the Circle. Communications in Partial Differential Equations, Taylor & Francis, 2005, 29 (3-4), pp.457-469. 〈10.1081/PDE-120030404〉. 〈hal-01251188〉
  • Patrick Bernard. The asymptotic behaviour of solutions of the forced Burgers equation on the circle. Nonlinearity, IOP Publishing, 2005, 18, pp.101-124. 〈10.1088/0951-7715/18/1/006〉. 〈hal-01251197〉
  • Patrick Bernard. The Action Spectrum Near Positive Definite Invariant Tori. Bulletin de la société mathématique de France, 2003, 131 (4), pp.603-616. 〈hal-01251171〉
  • Patrick Bernard. Homoclinic orbit to a center manifold. Calculus of Variations and Partial Differential Equations, 2003, 17 (2), pp.121-157. 〈10.1007/s00526-002-0162-0〉. 〈hal-01251761〉
  • Patrick Bernard. Une propriété de transfert en approximation diophantienne. Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc 2003, XII (4), pp.453-463. 〈hal-01251176〉
  • Patrick Bernard, Clodoaldo Grotta Ragazzo, Pedro Salamao. Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom. Asterisque, Société Mathématique de France, 2003, 286, pp.151-165. 〈hal-01251205〉
  • Patrick Bernard. Homoclinic Orbits in Families of Hypersurfaces with Hyperbolic Periodic Orbits. Journal of Differential Equations, Elsevier, 2002, 180 (2), pp.427-452. 〈10.1006/jdeq.2001.4062〉. 〈hal-01250629〉
  • Patrick Bernard. Connecting orbits of time dependent Lagrangian systems. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2002, 52 (5), pp.1533-1568. 〈hal-00294655〉
  • Patrick Bernard. Homoclinic orbits to invariant sets of quasi-integrable exact maps. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2000, 20 (6), pp.1583-1601. 〈hal-01251209〉
  • Patrick Bernard. Perturbation d'un hamiltonien partiellement hyperbolique. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1996, 323, pp.00. 〈hal-00294674〉

Communication dans un congrès2 documents

  • Patrick Bernard. Arnold's Diffusion: from the a priori unstable to the a priori stable case.. International Congress of Mathematicians, 2010, Hyderabad, India. Hindustan Book Agency, New Delhi., 3, pp.1680-1700, 2010. 〈hal-00678681〉
  • Patrick Bernard. Some remarks on the continuity equation. Séminaire: Équations aux Dérivées Partielles, Ecole Polytechnique., 2008, Palaiseau, France. 〈hal-00678723〉

Chapitre d'ouvrage1 document

  • Patrick Bernard. Hamiltonian Systems: Stability and Instability Theory. J.-P. Francoise, G.L. Naber and Tsou S.T. Encyclopedia of Mathematical Physics, Elsevier, pp.261, 2006. 〈hal-00294667〉

HDR1 document

  • Patrick Bernard. La dynamique des systèmes hamiltoniens presque intégrables. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2004. 〈tel-00008074〉