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dc.contributor.authorGiulietti, Paolopt_BR
dc.contributor.authorKloeckner, Benoît R.pt_BR
dc.contributor.authorLopes, Artur Oscarpt_BR
dc.contributor.authorFarias, Diego Marconpt_BR
dc.date.accessioned2018-09-22T03:01:36Zpt_BR
dc.date.issued2018pt_BR
dc.identifier.issn1435-9855pt_BR
dc.identifier.urihttp://hdl.handle.net/10183/182431pt_BR
dc.description.abstractGiven an onto map T acting on a metric space  and an appropriate Banach space of functions X./, one classically constructs for each potential A 2 X a transfer operator LA acting on X./. Under suitable hypotheses, it is well-known that LA has a maximal eigenvalue A, has a spectral gap and defines a unique Gibbs measure A. Moreover there is a unique normalized potential of the form B D ACf 􀀀f T Cc acting as a representative of the class of all potentials defining the same Gibbs measure. The goal of the present article is to study the geometry of the set N of normalized potentials, of the normalization map A 7! B, and of the Gibbs map A 7! A. We give an easy proof of the fact that N is an analytic submanifold of X and that the normalization map is analytic; we compute the derivative of the Gibbs map; and we endow N with a natural weak Riemannian metric (derived from the asymptotic variance) with respect to which we compute the gradient flow induced by the pressure with respect to a given potential, e.g. the metric entropy functional. We also apply these ideas to recover in a wide setting existence and uniqueness of equilibrium states, possibly under constraints.en
dc.format.mimetypeapplication/pdfpt_BR
dc.language.isoengpt_BR
dc.relation.ispartofJournal of the European Mathematical Society, JEMS. Zurique, Suíça, European Mathematical Society, 2018. Vol. 20, no. 10 (July 2018), p. 2357–2412pt_BR
dc.rightsOpen Accessen
dc.subjectTransfer operatorsen
dc.subjectEstados de equilibriopt_BR
dc.subjectEquilibrium statesen
dc.subjectEntropiapt_BR
dc.subjectEntropyen
dc.subjectRegularização entrópicapt_BR
dc.subjectRegularityen
dc.subjectWasserstein spaceen
dc.titleThe calculus of thermodynamical formalismpt_BR
dc.typeArtigo de periódicopt_BR
dc.identifier.nrb001077339pt_BR
dc.type.originEstrangeiropt_BR


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