Diffeomorphisms Holder conjugate to Anosov diffeomorphisms
Abstract
We show by means of a counterexample that a C1+Lip diffeomorphism Holder conjugate to an Anosov diffeomorphism is not necessarily Anosov. The counterexample can bear higher smoothness up to C3. Also we include a result from the 2006 Ph.D. thesis of T. Fisher: a C1+Lip diffeomorphism Holder conjugate to an Anosov diffeomorphism is Anosov itself provided that Holder exponents of the conjugacy and its inverse are sufficiently large.
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