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arXiv · 1710.03369

Maps in Dimension One with Infinite Entropy

Peter Hazard
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Abstract

We give examples of endomorphisms in dimension one with infinite topological entropy which are $\alpha$-H\"older and $(1,p)$-Sobolev for all $0\leq\alpha<1$ and $1\leq p<\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\alpha$-H\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.

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Peter Hazard. 2017-10-10. Maps in Dimension One with Infinite Entropy. https://arxiv.org/abs/1710.03369

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