Measures of maximal entropy for surface diffeomorphisms

• 成果类型: Article
• 署名作者: Buzzi, Jerome; Crovisier, Sylvain; Sarig, Omri
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.2.2
• 发表日期: 2022
• 页码: 421-508
• 关键词: unique equilibrium states; intrinsic ergodicity; symbolic dynamics; hyperbolic diffeomorphisms; zeta-functions; markov shifts; specification; EXISTENCE; systems; EXTENSIONS

摘要

We show that C-infinity-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do this we generalize Smale's spectral decomposition theorem to non-uniformly hyperbolic surface diffeomorphisms, we introduce homoclinic classes of measures, and we study their properties using codings by irreducible countable state Markov shifts.