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arXiv · 1607.02010

Topological invariance of the Collet-Eckmann condition for one-dimensional maps

Huaibin Li
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Abstract

This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several critical points the Collet-Eckmann condition is not in itself invariance under topological conjugacy. We show that the Collet-Eckmann condition together with any of several slow recurrence conditions is invariant under topological conjugacy. This extends and gives a new proof of a result by Luzzatto and Wang that also applies to the complex setting.

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Huaibin Li. 2016-07-07. Topological invariance of the Collet-Eckmann condition for one-dimensional maps. https://doi.org/10.1088/1361-6544/aa67a1

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