• Corpus ID: 119168266

# 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}
}
• Z. Kosloff
• Published 28 October 2014
• Mathematics
• arXiv: Dynamical Systems
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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