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Pré-Publication, Document De Travail Année : 2024

Higher Dimensional Birkhoff attractors

Résumé

We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We prove that this notion coincides with the classical Birkhoff attractor. We prove that for the dissipative system associated to the discounted Hamilton-Jacobi equation the graph of a solution is contained in the Birkhoff attractor. We also study what happens when we perturb a Hamiltonian system to make it dissipative and let the perturbation go to zero. The paper contains two important results on $\gamma$-supports and elements of the $\gamma$-completion of the space of exact Lagrangians. Firstly the $\gamma$-support of a Lagrangian in a cotangent bundle carries the cohomology of the base and secondly given an exact Lagrangian $L$, any Floer theoretic equivalent Lagrangian is the $\gamma$-limit of Hamiltonian images of $L$.

Dates et versions

hal-04529993 , version 1 (02-04-2024)

Identifiants

Citer

Marie-Claude Arnaud, Vincent Humilière, Claude Viterbo. Higher Dimensional Birkhoff attractors. 2024. ⟨hal-04529993⟩
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