Local stable and unstable sets for positive entropy C;dynamical systems  

作　　者：Shilin Feng Rui Gao Wen Huang Zeng Lian 

机构地区：[1]College of Mathematics,Sichuan University,Chengdu 610064,China [2]CAS Wu Wen-Tsun Key Laboratory of Mathematics,School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

出　　处：《Science China Mathematics》2022年第1期63-80,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11701394);supported by National Natural Science Foundation of China(Grant Nos.11971455 and 11731003);supported by National Natural Science Foundation of China(Grant Nos.11671279 and 11541003)。

摘　　要：For any C;diffeomorphism on a smooth compact Riemannian manifold that admits an ergodic measure with positive entropy,a lower bound of the Hausdorff dimension for the local stable and unstable sets is given in terms of the measure-theoretic entropy and the maximal Lyapunov exponent.The main line of our approach to this result is under the setting of topological dynamical systems,which is also applicable to infinite-dimensional C;dynamical systems.

关 键 词：local(un)stable set Hausdorff dimension measure-theoretic entropy maximal Lyapunov exponent 

分 类 号：O19[理学—数学]