SRB measures for pointwise hyperbolic systems on open regions  

作　　者：Jianyu Chen Huyi Hu Yunhua Zhou 

机构地区：[1]School of Mathematical Sciences&Center for Dynamical Systems and Di erential Equations,Soochow University,Suzhou 215006,China [2]Department of Mathematics,Michigan State University,East Lansing,MI 48824,USA [3]College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China

出　　处：《Science China Mathematics》2020年第9期1671-1720,共50页中国科学：数学（英文版）

基　　金：The third author was supported by National Natural Science Foundation of China(Grant Nos.11871120 and 11671093).

摘　　要：A diffeomorphism f:M→M is pointwise partially hyperbolic on an open invariant subset N⊂M if there is an invariant decomposition TNM=Eu⊕Ec⊕Es such that Dxf is strictly expanding on Eu x and contracting on Esx at each x∈N.We show that under certain conditions f has unstable and stable manifolds,and admits a nite or an in nite u-Gibbs measure μ.If f is pointwise hyperbolic on N,then μ is a Sinai-Ruelle-Bowen(SRB)measure or an in nite SRB measure.As applications,we show that some almost Anosov di eomorphisms and gentle perturbations of Katok's map have the properties.

关 键 词：pointwise hyperbolicity unstable manifold SRB measure almost Anosov di eomorphism Katok's map 

分 类 号：O186.11[理学—数学]