The dynamics of pseudographs in convex Hamiltonian systems

Details The dynamics of pseudographs in convex Hamiltonian systems The dynamics of pseudographs in convex Hamiltonian systems

2004-12-15

arxiv.org/abs/math/0412300v2

Journal of the American Mathematical Society 21, 3 (2008) 615-669

Mathematics

Dynamical Systems

Scientific paper

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.

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