Conservative anosov diffeomorphisms of T2 without an absolutely continuous invariant measure

Z. Kosloff*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)69-131
Number of pages63
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume54
Issue number1
DOIs
StatePublished - 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

Fingerprint

Dive into the research topics of 'Conservative anosov diffeomorphisms of T2 without an absolutely continuous invariant measure'. Together they form a unique fingerprint.

Cite this