Conservative Anosov diffeomorphisms of $T^2$ without an absolutely continuous invariant measure

Zemer Kosloff

doi:10.24033/asens.2456

Conservative Anosov diffeomorphisms of $T^2$ without an absolutely continuous invariant measure

Zemer Kosloff

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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 C^1+a Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C1 setting.

Original language	English
Pages (from-to)	69-131
Number of pages	73
Journal	Annales Scientifiques de l'École Normale Supérieure
Volume	4
Issue number	54
DOIs	https://doi.org/10.24033/asens.2456
Publication status	Published - 1 Feb 2021

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title = "Conservative Anosov diffeomorphisms of $T^2$ 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+a Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C1 setting.",

author = "Zemer Kosloff",

year = "2021",

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T1 - Conservative Anosov diffeomorphisms of $T^2$ without an absolutely continuous invariant measure

AU - Kosloff, Zemer

PY - 2021/2/1

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N2 - 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+a Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C1 setting.

AB - 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+a Anosov diffeomorphisms have a smooth invariant measure does not hold true in the C1 setting.

U2 - 10.24033/asens.2456

DO - 10.24033/asens.2456

M3 - Article (Academic Journal)

SN - 1873-2151

VL - 4

SP - 69

EP - 131

JO - Annales Scientifiques de l'École Normale Supérieure

JF - Annales Scientifiques de l'École Normale Supérieure

IS - 54

ER -

Conservative Anosov diffeomorphisms of $T^2$ without an absolutely continuous invariant measure

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