### Diffeomorphisms Holder conjugate to Anosov diffeomorphismsDiffeomorphisms Holder conjugate to Anosov diffeomorphisms

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 Author Gogolev, Andrey Source arXiv.org Content type Text File Format PDF Date of Submission 2008-09-02 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Dynamical Systems ♦ 37D25 ♦ 37D20 ♦ math Abstract We show by means of a counterexample that a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to $C^3$. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a $C^{1+Lip}$ diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large. Educational Use Research Learning Resource Type Thesis Page Count 15