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.
A., F., Giuliani, A., A., S. (2009). Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 8, 659-680 [10.2422/2036-2145.2009.4.03].
Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class
GIULIANI, ALESSANDRO;
2009-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
