On the Existence of SRB Measures for ∞ Surface Diffeomorphisms-Reference-Cited by-同舟云学术

On the Existence of SRB Measures for ∞ Surface Diffeomorphisms

Published:2022-10-05 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Buzzi Jérôme¹,Crovisier Sylvain¹,Sarig Omri²

Affiliation:

1. Laboratoire de Mathématiques d’Orsay , CNRS, UMR 8628 Université Paris-Saclay, Orsay 91405, France

2. Faculty of Mathematics and Computer Science , The Weizmann Institute of Science, Rehovot 7610001, Israel

Abstract

Abstract We give a proof of Viana’s [19] conjecture on physical measures, in the special case of $C^\infty $ surface diffeomorphisms, and using the analysis of entropy and Lyapunov exponents we developed in [5]. Burguet [3] has recently proved a stronger result, using a different method.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac275/46347272/rnac275.pdf

Reference22 articles.

1. SRB measures for partially hyperbolic systems whose central direction is mostly expanding;Alves;Invent. Math.,2000

2. SRB measures for partially hyperbolic systems whose central direction is mostly contracting;Bonatti;Israel J. Math.,2000

3. SRB measures for ${C}^{\infty }$ surface diffeomorphisms;Burguet

4. Measures of maximal entropy for surface diffeomorphisms;Buzzi;Ann. of Math. (2),2022

5. Continuity properties of Lyapunov exponents for surface diffeomorphisms;Buzzi;Invent. Math.,2022

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On physical measures of multi-singular hyperbolic vector fields;Transactions of the American Mathematical Society;2024-07-19

2. Persistent Non-statistical Dynamics in One-Dimensional Maps;Communications in Mathematical Physics;2024-04