Abstract
We prove rigidity results for a class of non-uniformly hyperbolic holomorphic maps. If a holomorphic Collet-Eckmann mapf is topologically conjugate to a holomorphic mapg, then the conjugacy can be improved to be quasiconformal. If there is only one critical point in the repeller, theng is Collet-Eckmann, too.
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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.
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Przytycki, F., Rohde, S. Rigidity of holomorphic Collet-Eckmann repellers. Ark. Mat. 37, 357–371 (1999). https://doi.org/10.1007/BF02412220
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DOI: https://doi.org/10.1007/BF02412220