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Gottschalk-Hedlund theorem revisited

dc.contributor.authorSU, Xifeng
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorTHIEULLEN, Philippe
dc.date.accessioned2024-04-04T02:55:57Z
dc.date.available2024-04-04T02:55:57Z
dc.date.created2019
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192414
dc.description.abstractEnErgodic optimization and discrete weak KAM theory are two parallel theories with several results in common. For instance, the Mather set is the locus of orbits which minimize the ergodic averages of a given observable. In the favorable cases, the observable is cohomologous to its ergodic minimizing value on the Mather set, and the discrete weak KAM solution plays the role of the transfer function. One possibility of construction of such a coboundary is by using the non linear Lax-Oleinik operator. The other possibility is by using a discounted cohomological equation. It is known that the discounted discrete weak KAM solution converges to some selected weak KAM solution. We show that, in the ergodic optimization case for a coboundary observable over a minimal system, the discounted transfer function converges if and only if the observable is balanced.
dc.language.isoen
dc.subject.enDynamical systems
dc.title.enGottschalk-Hedlund theorem revisited
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Systèmes dynamiques [math.DS]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02495323
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02495323v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=SU,%20Xifeng&THIEULLEN,%20Philippe&rft.genre=preprint


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