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|
|Number of pages||63|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - 2021|
Bibliographical noteFunding 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).
© 2021 Société Mathématique de France, Paris