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Quasisymmetric distortion and rigidity of expanding endomorphisms of 
Author(s):
Edson
de Faria
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1949-1957.
MSC (1991):
Primary 58F03, 30C62;
Secondary 26A16
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Abstract:
In this paper we examine a result of D. Sullivan according to which two  expanding endomorphisms of the circle are  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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Additional Information:
Edson
de Faria
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05389-970 São Paulo SP- Brasil
Email:
edson@ime.usp.br
DOI:
10.1090/S0002-9939-96-03218-2
PII:
S 0002-9939(96)03218-2
Keywords:
Expanding maps,
symmetric conjugacies
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 of article:
Copyright
1996,
American Mathematical Society
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