  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.
