SRB measures for C∞ surface diffeomorphisms

• 成果类型: Article; Early Access
• 署名作者: Burguet, David
• 署名单位: Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01235-7
• 发表日期: 2024
• 关键词: partially hyperbolic systems; central direction; entropy

摘要

AC(infinity) smooth surface diffeomorphism admits an SRB measure if and only if the set{x,lim sup(n)(1)/(n )log & Vert;d(x)f(n)& Vert;>0}has positive Lebesgue measure. Moreover the basinsof the ergodic SRB measures are covering this set Lebesgue almost everywhere. Wealso obtain similar results forCrsurface diffeomorphisms with+infinity>r>1.