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Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

Published online by Cambridge University Press:  23 June 2009

ANDREY GOGOLEV
ANDREY GOGOLEV*
Affiliation:
Mathematics Department, Penn State University, University Park, State College, PA 16802, USA (email: [email protected])
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Abstract

We show by means of a counterexample that a C1+Lip diffeomorphism Hölder conjugate to an Anosov diffeomorphism is not necessarily Anosov. Also we include a result from the 2006 PhD thesis of Fisher: a C1+Lip diffeomorphism Hölder conjugate to an Anosov diffeomorphism is Anosov itself provided that Hölder exponents of the conjugacy and its inverse are sufficiently large.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 2 , April 2010 , pp. 441 - 456
Copyright
Copyright © Cambridge University Press 2009

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