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Non-lacunary Gibbs Measures for Certain Fractal Repellers

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Abstract

In this paper, we study non-uniformly expanding repellers constructed as the limit sets for a non-uniformly expanding dynamical systems. We prove that given a Hölder continuous potential φ satisfying a summability condition, there exists non-lacunary Gibbs measure for φ, with positive Lyapunov exponents and infinitely many hyperbolic times almost everywhere. Moreover, this non-lacunary Gibbs measure is an equilibrium measure for φ.

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Authors and Affiliations

  1. Departamento de Matemática, IBILCE/UNESP, Rua Cristóvão Colombo 2265, 15054-000, S.J. Rio Preto, SP, Brazil

    Vanderlei Horita

  2. Departamento de Matemática, UFAL, Campus A.C. Simões, s/n, 57072-090, Maceió, Alagoas, Brazil

    Krerley Oliveira

Authors
  1. Vanderlei Horita
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  2. Krerley Oliveira
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Correspondence to Krerley Oliveira.

Additional information

Work partially supported by CAPES, CNPq, FAPESP, FAPEAL, and PRONEX/Faperj, Brazil.

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Horita, V., Oliveira, K. Non-lacunary Gibbs Measures for Certain Fractal Repellers. J Stat Phys 136, 842–863 (2009). https://doi.org/10.1007/s10955-009-9811-4

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  • DOI: https://doi.org/10.1007/s10955-009-9811-4

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