Arkiv för Matematik
- Ark. Mat.
- Volume 37, Number 2 (1999), 357-371.
Rigidity of holomorphic Collet-Eckmann repellers
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.
The first author acknowledges support by Polish KBN Grant 2 P03A 025 12 “Iterations of Holomorphic Functions” and support of the Hebrew University of Jerusalem, where a part of tha paper was written. The second author is grateful for the hospitality and support of the Caltech, where a part of the paper was written.
Ark. Mat., Volume 37, Number 2 (1999), 357-371.
Received: 8 August 1997
Revised: 22 June 1998
First available in Project Euclid: 31 January 2017
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1999 © Institut Mittag-Leffler
Przytycki, Feliks; Rohde, Steffen. Rigidity of holomorphic Collet-Eckmann repellers. Ark. Mat. 37 (1999), no. 2, 357--371. doi:10.1007/BF02412220. https://projecteuclid.org/euclid.afm/1485898640