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Paper detail

The maximal entropy measure detects non-uniform hyperbolicity

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.

preprint2010arXivOpen access
Juan Rivera-Letelier
math.CVmath.DS
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Juan Rivera-Letelier

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