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dc.contributor.authorSorrentino, Alfonso
dc.date.accessioned2013-10-15T14:24:49Z
dc.date.available2013-10-15T14:24:49Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11836
dc.language.isoenen
dc.subjectLiouville's theoremen
dc.subject.ddc519en
dc.titleOn the integrability of Tonelli Hamiltoniansen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this article we discuss a weaker version of Liouville's Theorem on the integrability of Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution hypothesis on the integrals of motion can be completely dropped and still interesting information on the dynamics of the system can be deduced. Moreover, we prove that on the $ n$-dimensional torus this weaker condition implies classical integrability in the sense of Liouville. The main idea of the proof consists in relating the existence of independent integrals of motion of a Tonelli Hamiltonian to the ``size'' of its Mather and Aubry sets. As a byproduct we point out the existence of ``non-trivial'' common invariant sets for all Hamiltonians that Poisson-commute with a Tonelli Hamiltonian.en
dc.relation.isversionofjnlnameTransactions of the American Mathematical Society
dc.relation.isversionofjnlvol363en
dc.relation.isversionofjnlissue10en
dc.relation.isversionofjnldate2011
dc.relation.isversionofjnlpages5071-5089en
dc.relation.isversionofdoihttp://dx.doi.org/10.1090/S0002-9947-2011-05492-9en
dc.identifier.urlsitehttp://arxiv.org/abs/0903.4300v2en
dc.relation.isversionofjnlpublisherAMSen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen


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