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Hausdorff Dimension of Non-Hyperbolic Repellers. I: Maps with Holes

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Abstract

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

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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. IMPA, Est. D. Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil

    Marcelo Viana

Authors
  1. Vanderlei Horita
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  2. Marcelo Viana
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Horita, V., Viana, M. Hausdorff Dimension of Non-Hyperbolic Repellers. I: Maps with Holes. Journal of Statistical Physics 105, 835–862 (2001). https://doi.org/10.1023/A:1013501211027

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  • DOI: https://doi.org/10.1023/A:1013501211027

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