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On the Continuity of the SRB Entropy for Endomorphisms

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Abstract

We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the dynamics. We apply our result to a vast class of non-uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the SRB measure. In particular, we show that the SRB entropy of Viana maps varies continuously with the map.

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Authors and Affiliations

  1. Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    José F. Alves

  2. Departamento de Matemática, Universidade Federal de Alagoas, Campus A. C. Simões s/n, 57000-000, Maceió, Brazil

    Krerley Oliveira

  3. Departamento de Matemática, ICMC-USP São Carlos, Caixa Postal 668, 13560-970, São Carlos, Brazil

    Ali Tahzibi

Authors
  1. José F. Alves
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  2. Krerley Oliveira
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  3. Ali Tahzibi
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Corresponding author

Correspondence to José F. Alves.

Additional information

Work carried out at USP-São Carlos, IMPA and University of Porto. JFA was partially supported by FCT through CMUP. AT was supported by FCT on leave from USP-São Carlos and Fapesp/Brazil (projeto temático 03/03107-9) and KO by Fapeal/Brazil and CNPq/Brazil.

Subjclass: 37C40, 37C75, 37D25

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Alves, J.F., Oliveira, K. & Tahzibi, A. On the Continuity of the SRB Entropy for Endomorphisms. J Stat Phys 123, 763–785 (2006). https://doi.org/10.1007/s10955-006-9059-1

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  • DOI: https://doi.org/10.1007/s10955-006-9059-1

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