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.
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.
Accepted:
Published online:
Marco Mazzucchelli 1; Alfonso Sorrentino 2
@article{CRMATH_2016__354_4_419_0, author = {Marco Mazzucchelli and Alfonso Sorrentino}, title = {Remarks on the symplectic invariance of {Aubry{\textendash}Mather} sets}, journal = {Comptes Rendus. Math\'ematique}, pages = {419--423}, publisher = {Elsevier}, volume = {354}, number = {4}, year = {2016}, doi = {10.1016/j.crma.2016.01.001}, language = {en}, }
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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