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 p. This result extends generically to the C°-closure of KAM tori.
Fathi, A., Giuliani, A., Sorrentino, A. (2009). Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, 8(4), 659-680.
Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class
SORRENTINO, ALFONSO
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 p. This result extends generically to the C°-closure of KAM tori.| File | Dimensione | Formato | |
|---|---|---|---|
|
FGS09.pdf
solo utenti autorizzati
Licenza:
Copyright dell'editore
Dimensione
166.32 kB
Formato
Adobe PDF
|
166.32 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
