Conservative anosov diffeomorphisms of T2 without an absolutely continuous invariant measure

Z. Kosloff

doi:10.24033/ASENS.2456

Conservative anosov diffeomorphisms of T² without an absolutely continuous invariant measure

Z. Kosloff^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We construct examples of C ¹ Anosov diffeomorphisms on T² which are of Krieger type III₁ with respect to Lebesgue measure. This shows that the Gurevic Oseledec phenomena that conservative C ¹C Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C ¹ setting.

Original language	American English
Pages (from-to)	69-131
Number of pages	63
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	54
Issue number	1
DOIs	https://doi.org/10.24033/ASENS.2456
State	Published - 2021

Bibliographical note

Funding Information:
Section 3 is part of the author’s PhD thesis in Tel Aviv University done under the supervision of Jon Aaronson. I would like to thank many people among them Jon Aaronson, Omri Sarig and Ian Melbourne for many helpful discussions and their continuous support. This research was supported in part by the European Advanced Grant StochExtHomog (ERC AdG 320977).

Publisher Copyright:
© 2021 Société Mathématique de France, Paris

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10.24033/ASENS.2456

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AB - We construct examples of C 1 Anosov diffeomorphisms on T2 which are of Krieger type III1 with respect to Lebesgue measure. This shows that the Gurevic Oseledec phenomena that conservative C 1C Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C 1 setting.

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Conservative anosov diffeomorphisms of T² without an absolutely continuous invariant measure

Abstract

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