A multiplicative ergodic theoretic characterization of relative equilibrium states

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dc.contributor.authorAntonioli, John
dc.contributor.authorHong, Soonjo
dc.contributor.authorQuas, Anthony
dc.date.accessioned2023-02-07T19:37:33Z
dc.date.available2023-02-07T19:37:33Z
dc.date.copyright2022en_US
dc.date.issued2022
dc.description.abstractIn this article, we continue the structural study of factor maps between symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type X (equipped with a potential function) to a sofic shift Z, equipped with a shift-invariant measure ν. We study relative equilibrium states, that is, shift-invariant measures on X that push forward under the factor map to ν which maximize the relative pressure: the relative entropy plus the integral of φ. In this paper, we establish a new connection to multiplicative ergodic theory by relating these factor triples to a cocycle of Ruelle–Perron–Frobenius operators, and showing that the principal Lyapunov exponent of this cocycle is the relative pressure; and the dimension of the leading Oseledets space is equal to the number of measures of relative maximal entropy, counted with a previously identified concept of multiplicity.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipFor S.H., funding was provided by Hongik University, Korea. A.Q.’s research was partially supported by NSERC.en_US
dc.identifier.citationAntonioli, J., Hong, S., & Quas, A. (2022). “A multiplicative ergodic theoretic characterization of relative equilibrium states.” Ergodic Theory and Dynamical Systems, 1-16. https://doi.org/10.1017/etds.2022.15en_US
dc.identifier.urihttps://doi.org/10.1017/etds.2022.15
dc.identifier.urihttp://hdl.handle.net/1828/14759
dc.language.isoenen_US
dc.publisherErgodic Theory and Dynamical Systemsen_US
dc.subjectrelative thermodynamic formalismen_US
dc.subjectmultiplicative ergodic theoryen_US
dc.subjecttransfer operatorsen_US
dc.titleA multiplicative ergodic theoretic characterization of relative equilibrium statesen_US
dc.typeArticleen_US

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