Rigidity of holomorphic Collet-Eckmann repellers

Feliks Przytycki Institute of Mathematics, Polish Academy of Sciences Steffen Rohde Department of Mathematics, Technische Universit├Ąt Berlin

TBD mathscidoc:1701.332921

Arkiv for Matematik, 37, (2), 357-371, 1997.8
We prove rigidity results for a class of non-uniformly hyperbolic holomorphic maps. If a holomorphic Collet-Eckmann map$f$is topologically conjugate to a holomorphic map$g$, then the conjugacy can be improved to be quasiconformal. If there is only one critical point in the repeller, then$g$is Collet-Eckmann, too.
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@inproceedings{feliks1997rigidity,
  title={Rigidity of holomorphic Collet-Eckmann repellers},
  author={Feliks Przytycki, and Steffen Rohde},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556643784730},
  booktitle={Arkiv for Matematik},
  volume={37},
  number={2},
  pages={357-371},
  year={1997},
}
Feliks Przytycki, and Steffen Rohde. Rigidity of holomorphic Collet-Eckmann repellers. 1997. Vol. 37. In Arkiv for Matematik. pp.357-371. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203556643784730.
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