Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

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 H...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2010-04, Vol.30 (2), p.441-456
Main Author: GOGOLEV, ANDREY
Format: Article
Language:English
Subjects:
Dynamical systems
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Summary: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385709000169