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Random composition of two rational maps: Singularity of the invariant measure

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Abstract

We study the invariant measure of a Markov chain obtained by randomly composing two rational maps related to the Anderson model with a Bernoulli potential. For a certain range of the parameters we show that the invariant measure is singular continuous. In certain cases the support turns out to be a Cantor set with a multifractal structure.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universita' di Roma “La Sapienza”, 00185, Rome, Italy

    F. Martinelli

  2. Dipartimento di Fisica, Universita' di Roma “La Sapienza”, 00185, Rome, Italy

    E. Scoppola

  3. GNSM-CNR, Italy

    E. Scoppola

Authors
  1. F. Martinelli
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  2. E. Scoppola
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Martinelli, F., Scoppola, E. Random composition of two rational maps: Singularity of the invariant measure. J Stat Phys 50, 1021–1042 (1988). https://doi.org/10.1007/BF01019151

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  • DOI: https://doi.org/10.1007/BF01019151

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