The dynamics of pseudographs in convex Hamiltonian systems
By P. Bernard. 2004
138 citations recorded by the source corpus.
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.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/eb5b863c87423453fd0d3622831bd1a72f7a1ac1
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- A strong form of Arnold diusion for two and a half degrees of freedom (2012, methodology): “In [9] for two cohomologies c, c′ ∈ H(1)(T(2),R) a forcing relation c ` c′ is introduced.”
- Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders (2016, methodology): “ow that this cylinlder C contains a family of Man˜´e sets N˜(c), c∈ Γ, each being of Aubry-Mather type, i.e. a Lipschitz graph over the circle (see Theorem 1.4). • Using the notion of a forcing class [Be1] generically construct orbits diffusing along this cylinder C (see Theorem 1.5). 1.4.1 Existence”
- Optimal mass transportation and Mather theory (2004, background): “ K. A function u: M×]0,T[−→ M is called locally semi-concave if it is semi-concave on each M×[s,t], for 0 <s<t<T. The following regularity result follows from Fathi’s work, see [20] and also [8]. Proposition 13. Let u1 and u2 be two K-semi-concave functions. Let Abe the set of minima of the”