General multifractal analysis of local entropies

Volume 165 / 2000

Floris Takens, Evgeny Verbitski Fundamenta Mathematicae 165 (2000), 203-237 DOI: 10.4064/fm-165-3-203-237

Abstract

We address the problem of the multifractal analysis of local entropies for arbitrary invariant measures. We obtain an upper estimate on the multifractal spectrum of local entropies, which is similar to the estimate for local dimensions. We show that in the case of Gibbs measures the above estimate becomes an exact equality. In this case the multifractal spectrum of local entropies is a smooth concave function. We discuss possible singularities in the multifractal spectrum and their relation to phase transitions.

Authors

  • Floris Takens
  • Evgeny Verbitski

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