The dynamics of pseudographs in convex Hamiltonian systems

Abstract : We study the evolution, under convex Hamiltonian flows on cotangent bundles of compact manifolds, of certain distinguished subsets of the phase space. These subsets are generalizations of Lagrangian graphs, we call them pseudographs. They emerge in a natural way from Fathi's weak KAM theory. By this method, we find various orbits which connect prescribed regions of the phase space. Our study is inspired by works of John Mather. As an application, we obtain the existence of diffusion in a large class of a priori unstable systems and provide a solution to the large gap problem. We hope that our method will have applications to more examples.
Document type :
Journal articles
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download
Contributor : Patrick Bernard <>
Submitted on : Thursday, July 10, 2008 - 9:50:17 AM
Last modification on : Wednesday, February 19, 2020 - 8:58:33 AM
Long-term archiving on: Tuesday, September 21, 2010 - 5:09:31 PM


Files produced by the author(s)




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⟩



Record views


Files downloads