# Conservative Anosov diffeomorphisms of the two torus without an absolutely continuous invariant measure

@article{Kosloff2014ConservativeAD, title={Conservative Anosov diffeomorphisms of the two torus without an absolutely continuous invariant measure}, author={Zemer Kosloff}, journal={arXiv: Dynamical Systems}, year={2014} }

We construct examples of $C^{1}$ Anosov diffeomorphisms on $\mathbb{T}^{2}$ which are of Krieger type ${\rm III}_{1}$ with respect to Lebesgue measure. This shows that the Gurevic Oseledec phenomena that conservative $C^{1+\alpha}$ Anosov diffeomorphisms have a smooth invariant measure does not hold true in the $C^{1}$ setting.

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