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General multifractal analysis of local entropies

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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.
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  • Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands,
  • Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands,
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