Existence of periodic orbits and horseshoes for mappings in a separable Banach space

被引：7

作者：

Lian, Zeng ^{[1
]}

Ma, Xiao ^{[2
]}

机构：

[1] Sichuan Univ, Coll Math Sci, Chengdu 610016, Sichuan, Peoples R China

[2] Univ Sci & Technol China, Sch Math Sci, Wu Wen Tsun Key Lab Math, Hefei, Anhui, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 12期

关键词：

LYAPUNOV EXPONENTS; DYNAMICAL-SYSTEMS; INVARIANT-MANIFOLDS; ENTROPY; AXIOM;

D O I：

10.1016/j.jde.2020.08.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a smooth map in a separable Banach space with a hyperbolic invariant measure, we mainly prove that positivity of the measure-theoretic entropy of the hyperbolic measure implies the existence of periodic orbits and horseshoes. This is an extension of Lian and Young's work on maps in a Hilbert space to the case of systems on a Banach space. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：11694 / 11738

页数：45

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