Diffeomorphisms Holder conjugate to Anosov diffeomorphisms
classification
🧮 math.DS
keywords
anosovdiffeomorphismholderconjugatecounterexamplediffeomorphismsbearconjugacy
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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.
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