Maps in dimension one with infinite entropy

DOI10.4310/ARKIV.2020.V58.N1.A7zbMATH Open1464.37024arXiv1710.03369MaRDI QIDQ2180944

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Publication date: 18 May 2020

Published in: (Search for Journal in Brave)

Abstract: We give examples of endomorphisms in dimension one with infinite topological entropy which are $alpha$-H"older and $(1,p)$-Sobolev for all $0leqalpha<1$ and $1leqp<infty$. 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.

Full work available at URL: https://arxiv.org/abs/1710.03369

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