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Patrick Bernard, Publications

Preprints, Working Papers, ...3 documents

  • Shahriar Aslani, Patrick Bernard. Normal form near orbit segments of convex Hamiltonian systems.. 2020. ⟨hal-02550940v2⟩
  • Tiphaine Jézéquel, Patrick Bernard, Éric Lombardi. Homoclinic connections with many loops near a $0^2 iw$ resonant fixed point for Hamiltonian systems. 2014. ⟨hal-01045008⟩
  • Patrick Bernard, Maxime Zavidovique. Regularization of subsolutions in discrete weak KAM theory. 2012. ⟨hal-00865241⟩

Journal articles39 documents

  • Patrick Bernard, Stefan Suhr. Cauchy and uniform temporal functions of globally hyperbolic cone fields. Proceedings of the American Mathematical Society, American Mathematical Society, In press. ⟨hal-02129166v2⟩
  • Patrick Bernard, Stefan Suhr. Smoothing causal functions. Journal of Physics: Conference Series, IOP Publishing, 2018, 968, pp.012001. ⟨10.1088/1742-6596/968/1/012001⟩. ⟨hal-01633180v2⟩
  • Patrick Bernard, Stefan Suhr. Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions.. Communications in Mathematical Physics, Springer Verlag, 2018, 359 (2), pp.467-498. ⟨10.1007/s00220-018-3127-7⟩. ⟨hal-01487859v3⟩
  • 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, 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⟩
  • Patrick Bernard. Formes normales de champs de vecteurs . Gazette des Mathématiciens, Société Mathématique de France, 2016. ⟨hal-01435605⟩
  • 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⟩
  • Véronique Charbonnier, Judith Monnier, Junxian Zhang, Valérie Paul-Boncour, Suzanne Joiret, et al.. Relationship between H2 sorption properties and aqueous corrosion mechanisms in A2Ni7 hydride forming alloys (A = Y, Gd or Sm). Journal of Power Sources, Elsevier, 2016, 326, pp.146-155. ⟨10.1016/j.jpowsour.2016.06.126⟩. ⟨hal-01344775⟩
  • 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, 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. 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, 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. The Lax–Oleinik semi-group: a Hamiltonian point of view. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), 2012, 142 (6), pp.1131-1177. ⟨10.1017/S0308210511000059⟩. ⟨hal-00678990v2⟩
  • 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, 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⟩
  • Patrick Bernard. Lasry-Lions Regularization and a Lemma of Ilmanen. Rendiconti del Seminario Matematico della Università di Padova, University of Padua / European Mathematical Society, 2010, 124, pp.221-229. ⟨10.4171/RSMUP/124-15⟩. ⟨hal-00448255v2⟩
  • 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. 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. 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, 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⟩
  • 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. 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. 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. 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. 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. 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. 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, 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. 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, 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. Homoclinic orbit to a center manifold. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2003, 17 (2), pp.121-157. ⟨10.1007/s00526-002-0162-0⟩. ⟨hal-01251761⟩
  • 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. 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. The Action Spectrum Near Positive Definite Invariant Tori. Bulletin de la société mathématique de France, Société Mathématique de France, 2003, 131 (4), pp.603-616. ⟨hal-01251171⟩
  • 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 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. 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⟩

Conference papers2 documents

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

Book sections1 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⟩

Habilitation à diriger des recherches1 document

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