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A theorem of measurable rigidity in Diff ^{\omega} (\mathbb{S}^1)}

Published online by Cambridge University Press:  02 October 2001

JULIO C. REBELO
JULIO C. REBELO
Affiliation:
Pontificia Universidade Catolica do Rio de Janeiro PUC-Rio, Rua Marquês de São Vicente 225 - Gávea, Rio de Janeiro, RJ 22453-900, Brazil (e-mail: jrebelo@mat.puc-rio.br) Present address: IMS - Math. Tower, State University of New York at Stony Brook, Stony Brook, NY 11794-3660, USA (e-mail: jrebelo@math.sunysb.edu)
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Abstract

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We consider measurable conjugacies between two non-solvable subgroups G_1, G_2 of the group of analytic diffeomorphisms of the circle which admit a finite generating set close to the identity. These measurable conjugacies are characterized by our main result which asserts that, up to finite coverings, they coincide almost everywhere with an analytic diffeomorphism of the circle.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 5 , October 2001 , pp. 1525 - 1561
Copyright
2001 Cambridge University Press