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

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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	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

All Science Journal Classification (ASJC) codes

General Mathematics

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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.",

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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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