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The maximal entropy measure detects non-uniform hyperbolicity

Authors
  • Rivera-Letelier, Juan
Type
Preprint
Publication Date
May 14, 2010
Submission Date
May 14, 2010
Identifiers
arXiv ID: 1005.2640
Source
arXiv
License
Yellow
External links

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. 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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