- 04-313 Bernard patrick
- The dynamics of pseudographs in convex Hamiltonian systems
Sep 30, 04
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Abstract. We study the evolution, under convex Hamiltonian flows on cotangent
bundles of compact manifolds, of certain distinguished subsets of the
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.