Maps in dimension one with infinite entropy

Peter Hazard Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, Brazil

Functional Analysis mathscidoc:2203.12002

Arkiv for Matematik, 58, (1), 94-119, 2020.4
For each real α,0≤α<1, we give examples of endomorphisms in dimension one with infinite topological entropy which are α‑Hölder; and for each real p,1≤p<∞, we also give examples of endomorphisms in dimension one with infinite topological entropy which are (1,p)-Sobolev. These examples are constructed within a family of endomorphisms with infinite topological entropy and which traverse all α-Hölder 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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@inproceedings{peter2020maps,
  title={Maps in dimension one with infinite entropy},
  author={Peter Hazard},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310170023613048935},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={1},
  pages={94-119},
  year={2020},
}
Peter Hazard. Maps in dimension one with infinite entropy. 2020. Vol. 58. In Arkiv for Matematik. pp.94-119. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220310170023613048935.
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