Mixing $C^r$ maps of the interval without maximal measure

Sylvie Ruette

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arXiv · 1901.00325

Mixing $C^r$ maps of the interval without maximal measure

Sylvie Ruette

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Abstract

We construct a $C^r$ transformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy. Whereas the assumption of $C^{\infty}$ ensures existence of maximal measures for an interval map, it shows we cannot weaken the smoothness assumption. We also compute the local entropy of the example.

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Sylvie Ruette. 2019-01-02. Mixing $C^r$ maps of the interval without maximal measure. https://arxiv.org/abs/1901.00325

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