Given a smooth compact Riemannian manifold and a Hamiltonian on the cotangent space , 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 . This result extends generically to the -closure of KAM tori.
@article{ASNSP_2009_5_8_4_659_0,
author = {Fathi, Albert and Giuliani, Alessandro and Sorrentino, Alfonso},
title = {Uniqueness of invariant {Lagrangian} graphs in a homology or a cohomology class},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {659--680},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 8},
number = {4},
year = {2009},
mrnumber = {2647908},
zbl = {1192.37086},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0/}
}
TY - JOUR AU - Fathi, Albert AU - Giuliani, Alessandro AU - Sorrentino, Alfonso TI - Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2009 SP - 659 EP - 680 VL - 8 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0/ LA - en ID - ASNSP_2009_5_8_4_659_0 ER -
%0 Journal Article %A Fathi, Albert %A Giuliani, Alessandro %A Sorrentino, Alfonso %T Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2009 %P 659-680 %V 8 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0/ %G en %F ASNSP_2009_5_8_4_659_0
Fathi, Albert; Giuliani, Alessandro; Sorrentino, Alfonso. Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 4, pp. 659-680. http://www.numdam.org/item/ASNSP_2009_5_8_4_659_0/
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