Local stable and unstable sets for positive entropy C1 dynamical systems

被引：0
|
作者：
Shilin Feng
Rui Gao
Wen Huang
Zeng Lian
机构：
[1] Sichuan University,College of Mathematics
[2] University of Science and Technology of China,CAS Wu Wen
来源：
Science China Mathematics | 2022年 / 65卷
关键词：
local (un)stable set; Hausdorff dimension; measure-theoretic entropy; maximal Lyapunov exponent; 37A35; 37C45; 37D25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For any C1 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 C1 dynamical systems.
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页码：63 / 80
页数：17
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