THE MAXIMAL ENTROPY MEASURE DETECTS NON-UNIFORM HYPERBOLICITY
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Date
2010
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INT PRESS BOSTON, INC
Abstract
We characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure.
With the same tools we give an extension of the result of Carleson, Jones and Yoccoz that semi-hyperbolicity characterizes those polynomial maps whose basin of attraction of infinity is a John domain, to rational maps having a completely invariant attracting basin.
With the same tools we give an extension of the result of Carleson, Jones and Yoccoz that semi-hyperbolicity characterizes those polynomial maps whose basin of attraction of infinity is a John domain, to rational maps having a completely invariant attracting basin.
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Keywords
Non-uniform hyperbolicity, maximal entropy measure, Julia set, doubling measure, JULIA SETS, COLLET-ECKMANN, RATIONAL FUNCTIONS, UNIFORMLY PERFECT, MAPS, POROSITY, DYNAMICS, HOLDER, DISKS