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Statistical Stability and Continuity of SRB Entropy for Systems with Gibbs-Markov Structures

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Abstract

We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an application we consider the family of Hénon maps within the set of Benedicks-Carleson parameters.

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Authors and Affiliations

  1. Centro de Matemática da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal

    José F. Alves, Maria Carvalho & Jorge Milhazes Freitas

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  1. José F. Alves
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  2. Maria Carvalho
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  3. Jorge Milhazes Freitas
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Correspondence to Jorge Milhazes Freitas.

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Communicated by G. Gallavotti

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Alves, J.F., Carvalho, M. & Freitas, J.M. Statistical Stability and Continuity of SRB Entropy for Systems with Gibbs-Markov Structures. Commun. Math. Phys. 296, 739–767 (2010). https://doi.org/10.1007/s00220-010-1027-6

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  • DOI: https://doi.org/10.1007/s00220-010-1027-6

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