The maximal entropy measure detects non-uniform hyperbolicity

Details The maximal entropy measure detects non-uniform hyperbolicity The maximal entropy measure detects non-uniform hyperbolicity

2010-05-14

arxiv.org/abs/1005.2640v1

Mathematics

Dynamical Systems

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Scientific paper

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. Using the same tools in the proof of these results we give an extension of a 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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