Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class
A Fathi, A Giuliani, A Sorrentino - … Normale Superiore di Pisa-Classe di …, 2009 - numdam.org
A Fathi, A Giuliani, A Sorrentino
Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2009•numdam.orgGiven a smooth compact Riemannian manifold M and a Hamiltonian H on the cotangent
space T∗ M, strictly convex and superlinear in the momentum variables, we prove
uniqueness of certain “ergodic” invariant Lagrangian graphs within a given homology or
cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our
result implies global uniqueness of Lagrangian KAM tori with rotation vector ρ. This result
extends generically to the C0-closure of KAM tori.
space T∗ M, strictly convex and superlinear in the momentum variables, we prove
uniqueness of certain “ergodic” invariant Lagrangian graphs within a given homology or
cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our
result implies global uniqueness of Lagrangian KAM tori with rotation vector ρ. This result
extends generically to the C0-closure of KAM tori.
Abstract
Given a smooth compact Riemannian manifold M and a Hamiltonian H on the cotangent space T∗ M, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain “ergodic” invariant Lagrangian graphs within a given homology or cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our result implies global uniqueness of Lagrangian KAM tori with rotation vector ρ. This result extends generically to the C0-closure of KAM tori.
numdam.org
以上显示的是最相近的搜索结果。 查看全部搜索结果