Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class

Abstract

Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^{\ast }M$, 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 $\rho$. This result extends generically to the $C^0$-closure of KAM tori.

20 pages. Version published on Ann. Sc. Norm. Super. Pisa Cl. Sci.(5) Vol. 8, no. 4, 659-680, 2009

References in corpus (1)

• Hyperbolic low-dimensional invariant tori and summations of divergent series

Cited by in corpus (2)

• Quasi-periodic motions in dynamical systems. Review of a renormalisation group approach
• Analytic Lagrangian tori for the planetary many-body problem