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Multifractal Nonrigidity of Topological Markov Chains

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Abstract

Given a multifractal spectrum, we consider the problem of whether it is possible to recover the potential that originates the spectrum. The affirmative solution of this problem would correspond to a “multifractal” classification of dynamical systems, i.e., a classification solely based on the information given by multifractal spectra. For the entropy spectrum on topological Markov chains we show that it is possible to have both multifractal rigidity and multifractal “nonrigidity”, by appropriately varying the Markov chain and the potential defining the spectrum. The “nonrigidity” even occurs in some generic sense. This strongly contrasts to the usual opinion among some experts that it should be possible to recover the potential up to some equivalence relation, at least in some generic sense.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal

    Luis Barreira & Vitor Saraiva

Authors
  1. Luis Barreira
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  2. Vitor Saraiva
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Corresponding author

Correspondence to Luis Barreira.

Additional information

Supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems, through FCT by Program POCTI/FEDER and the grant SFRH/BD/10154/2002.

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Barreira, L., Saraiva, V. Multifractal Nonrigidity of Topological Markov Chains. J Stat Phys 130, 387–412 (2008). https://doi.org/10.1007/s10955-007-9429-3

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  • DOI: https://doi.org/10.1007/s10955-007-9429-3

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