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Rigidity of critical circle mappings II

Author(s): Edson de Faria; Welington de Melo
Journal: J. Amer. Math. Soc. 13 (2000), 343-370.
MSC (2000): Primary 37F25; Secondary 37E10, 30D05, 37F40
Posted: November 23, 1999
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Abstract: We prove that any two real-analytic critical circle maps with cubic critical point and the same irrational rotation number of bounded type are $C^{1+\alpha }$ conjugate for some $\alpha >0$.

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Additional Information:

Edson de Faria
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP05508-900 São Paulo SP - Brasil
Email: edson@ime.usp.br

Welington de Melo
Affiliation: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, CEP22460-320 Rio de Janeiro RJ - Brasil
Email: demelo@impa.br

DOI: 10.1090/S0894-0347-99-00324-0
PII: S 0894-0347(99)00324-0
Keywords: Holomorphic pairs, complex bounds, uniform twist, rigidity
Received by editor(s): November 9, 1998
Received by editor(s) in revised form: September 20, 1999
Posted: November 23, 1999
Additional Notes: This work has been partially supported by the Pronex Project on Dynamical Systems, by FAPESP Grant 95/3187-4 and by CNPq Grant 30.1244/86-3.
Copyright of article: Copyright 2000, American Mathematical Society

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