Conservative Anosov diffeomorphisms of the two torus without an absolutely continuous invariant measure
Abstract
We construct examples of C1 Anosov diffeomorphisms on T2 which are of Krieger type III1 with respect to Lebesgue measure. This shows that the Gurevic Oseledec phenomena that conservative C1+α Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C1 setting.
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