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

共 8 条

[1] Existence of periodic orbits and horseshoes for semiflows on a separable Banach space
Ma, Xiao
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022, 61 (06)
[2] Lyapunov Exponents, Periodic Orbits and Horseshoes for Mappings of Hilbert Spaces
Lian, Zeng
Young, Lai-Sang
ANNALES HENRI POINCARE, 2011, 12 (06): : 1081 - 1108
[3] The existence of semi-horseshoes for C1 partially hyperbolic attractors in a Banach space
Zhang, Jianhua
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 518 (02)
[4] LYAPUNOV EXPONENTS, PERIODIC ORBITS, AND HORSESHOES FOR SEMIFLOWS ON HILBERT SPACES
Lian, Zeng
Young, Lai-Sang
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 25 (03) : 637 - 665
[5] Existence of periodic orbits of stable saturated systems
Moreno, I
Suárez, R
SYSTEMS & CONTROL LETTERS, 2004, 51 (3-4) : 293 - 309
[6] Existence and uniqueness of global Koopman eigenfunctions for stable fixed points and periodic orbits
Kvalheim, Matthew D.
Revzen, Shai
PHYSICA D-NONLINEAR PHENOMENA, 2021, 425
[7] Spatial periodic orbits in the equilateral circular restricted four-body problem: computer-assisted proofs of existence
Burgos-Garcia, Jaime
Lessard, Jean-Philippe
James, J. D. Mireles
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2019, 131 (01)
[8] Unstable Manifolds of Relative Periodic Orbits in the Symmetry-Reduced State Space of the Kuramoto-Sivashinsky System
Budanur, Nazmi Burak
Cvitanovic, Predrag
JOURNAL OF STATISTICAL PHYSICS, 2017, 167 (3-4) : 636 - 655

← 1 →