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Topological invariance of generic non-uniformly expanding multimodal maps

Stefano Luzzatto·Lanyu Wang
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Abstract

We show that a strengthened version of the Collet-Eckmann condition for multimodal maps is topologically invariant. In particular, if f is non-uniformly expanding and the critical points are generic with respect to the absolutely continuous invariant measure, then any map g topologically conjugate to f is also non-uniformly expanding.

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Stefano Luzzatto, Lanyu Wang. 2003-07-02. Topological invariance of generic non-uniformly expanding multimodal maps. https://arxiv.org/abs/math/0307030

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