Ergodic Theory and Dynamical Systems

Research Article

Diffeomorphisms Hölder conjugate to Anosov diffeomorphisms

ANDREY GOGOLEVa1

a1 Mathematics Department, Penn State University, University Park, State College, PA 16802, USA (email: agogolev@math.psu.edu)

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.

(Received September 08 2008)

(Revised February 09 2009)