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Fractal dimensions and homeomorphic conjugacies

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Abstract

We investigate the behavior of the spectrum of singularities associated with the invariant measure of some dynamical systems under nonsmooth coordinate changes. When the homeomorphic conjugacy is not Lipschitz continuous, we discuss how its singularities can affect the whole set of generalized fractal dimensions. We give applications to homeomorphisms that conjugate critical circle maps with irrational (golden mean) winding numbers. We present numerical studies corroborating the theoretical predictions.

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Author notes

  1. A. Arneodo

    Present address: Laboratoire de Physique Théorique, Université de Nice, 06034, Nice, France

  2. M. Holschneider

    Present address: Mathematisches Institut, Ruhr Universitat, 8630, Bochum 1, Germany

Authors and Affiliations

  1. Center for Nonlinear Dynamics, Physics Department, University of Texas, 78712, Austin, Texas

    A. Arneodo

  2. Centre de Physique Théorique, CNRS-Luminy, Case 907, 13288, Marseille, France

    M. Holschneider

Authors
  1. A. Arneodo
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  2. M. Holschneider
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Arneodo, A., Holschneider, M. Fractal dimensions and homeomorphic conjugacies. J Stat Phys 50, 995–1020 (1988). https://doi.org/10.1007/BF01019150

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  • DOI: https://doi.org/10.1007/BF01019150

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