Abstract
In this paper we establish the complete multifractal formalism for equilibrium measures for Hölder continuous conformal expanding maps andexpanding Markov Moran-like geometric constructions. Examples include Markov maps of an interval, beta transformations of an interval, rational maps with hyperbolic Julia sets, and conformal toral endomorphisms. We also construct a Hölder continuous homeomorphism of a compact metric space with an ergodic invariant measure of positive entropy for which the dimension spectrum is not convex, and hence the multifractal formalism fails.
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Pesin, Y., Weiss, H. A multifractal analysis of equilibrium measures for conformal expanding maps and Moran-like geometric constructions. J Stat Phys 86, 233–275 (1997). https://doi.org/10.1007/BF02180206
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DOI: https://doi.org/10.1007/BF02180206