Quasisymmetric distortion and rigidity of expanding endomorphisms of $S^1$
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- by Edson de Faria
- Proc. Amer. Math. Soc. 124 (1996), 1949-1957
- DOI: https://doi.org/10.1090/S0002-9939-96-03218-2
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Abstract:
In this paper we examine a result of D. Sullivan according to which two $C^{1+\alpha }$ expanding endomorphisms of the circle are $C^{1+\alpha }$ conjugate as soon as they are symmetrically conjugate. We develop general a priori estimates on the local distortion of quasisymmetric mappings and combine them with the classical naive distortion lemma to present a complete proof of Sullivan’s result. A new proof is offered at the end that renders unnecessary the use of Markov partitions or the control of eigenvalues at periodic points.References
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Bibliographic Information
- Edson de Faria
- Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05389-970 São Paulo SP- Brasil
- MR Author ID: 357550
- Email: edson@ime.usp.br
- Received by editor(s): November 21, 1994
- Additional Notes: This work is part of Projeto Temático de Equipe “Transição de Fase Dinâmica em Sistemas Evolutivos”, supported by FAPESP Grant 90/3918-5.
- Communicated by: Linda Keen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1949-1957
- MSC (1991): Primary 58F03, 30C62; Secondary 26A16
- DOI: https://doi.org/10.1090/S0002-9939-96-03218-2
- MathSciNet review: 1307509