Remarks on the symplectic invariance of Aubry–Mather sets

Marco Mazzucchelli; Alfonso Sorrentino

doi:10.1016/j.crma.2016.01.001

Differential geometry/Dynamical systems

Remarks on the symplectic invariance of Aubry–Mather sets
[Remarques sur l'invariance symplectique des ensembles d'Aubry–Mather]

Présenté par : Charles-Michel Marle

Marco Mazzucchelli ¹ ; Alfonso Sorrentino ²

¹ CNRS and UMPA, École normale Supérieure de Lyon, France
² Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, Italy

Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 419-423.

Résumé
Abstract

On discute et clarifie quelques questions liées à la généralisation du théorème de Bernard sur l'invariance symplectique des ensembles d'Aubry, de Mather et de Mañé aux cas de classes de cohomologie non nulles et de symplectomorphismes non exacts et non nécessairement homotopes à l'identité.

In this note, we discuss and clarify some issues related to the generalization of Bernard's theorem on the symplectic invariance of Aubry, Mather and Mañé sets, to the cases of non-zero cohomology classes or non-exact symplectomorphisms, not necessarily homotopic to the identity.

Reçu le : 2015-05-06
Accepté le : 2016-01-12
Publié le : 2016-02-11

DOI : 10.1016/j.crma.2016.01.001

Affiliations des auteurs :

Marco Mazzucchelli ¹ ; Alfonso Sorrentino ²

¹ CNRS and UMPA, École normale Supérieure de Lyon, France
² Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”, Italy

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     title = {Remarks on the symplectic invariance of {Aubry{\textendash}Mather} sets},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {419--423},
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Marco Mazzucchelli; Alfonso Sorrentino. Remarks on the symplectic invariance of Aubry–Mather sets. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 419-423. doi : 10.1016/j.crma.2016.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.01.001/

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