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Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms

dc.contributor.authorViterbo, Claude
HAL ID: 20809
ORCID: 0000-0001-5764-8391
dc.contributor.authorSorrentino, Alfonso
dc.date.accessioned2010-04-07T10:16:58Z
dc.date.available2010-04-07T10:16:58Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3871
dc.language.isoenen
dc.subjectAsymptotic Hofer distanceen
dc.subjectaction-minimizing measure
dc.subjectsymplectic homogenization
dc.subjectMather's beta function
dc.subjectMather's minimal average action
dc.subjectViterbo distance
dc.subjectMather theory
dc.subjectAubry–Mather theory
dc.subject.ddc515en
dc.titleAction minimizing properties and distances on the group of Hamiltonian diffeomorphismsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn this article we prove that for a smooth fiberwise convex Hamiltonian, the asymptotic Hofer distance from the identity gives a strict upper bound to the value at $0$ of Mather's $\beta$ function, thus providing a negative answer to a question asked by K. Siburg in \cite{Siburg1998}. However, we show that equality holds if one considers the asymptotic distance defined in \cite{Viterbo1992}.en
dc.relation.isversionofjnlnameGeometry and Topology
dc.relation.isversionofjnlvol14
dc.relation.isversionofjnlissue4
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages2383–2403
dc.relation.isversionofdoihttp://dx.doi.org/10.2140/gt.2010.14.2383
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00458323/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherMathematical Sciences Publishers
dc.subject.ddclabelAnalyseen


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