| A Multifractal Analysis Of Gibbs Measures For Conformal Expanding Maps And Markov Moran Geometric Constructions (1997) | |||||||||||||||
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| . We establish the complete multifractal formalism for Gibbs measures for conformal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic Julia sets, and conformal toral endomorphisms. I: Introduction This paper describes the multifractal analysis of measures invariant under dynamical systems. The concept of a multifractal analysis was suggested by several physicists in the seminal paper [HJKPS] and became a popular interdisciplinary subject of study. A search of several electronic databases showed that there are now hundreds of related papers in the physical and mathematical literature. The first rigorous multifractal analysis was carried out in [CLP] for a special class of measures invariant under some one-dimensional Markov maps, and in [Ra] for Gibbs measures for Cookie-Cutter maps. Lopes [Lo] studied the measure of maximal entropy for a hyperbolic Julia set. Recently, Simpelaere [Si] effected a complete multifractal analy... | |||||||||||||||
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