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 50 条

[21] Periodic orbits and invariant surfaces of nonlinear mappings
Vrahatis, MN
Bountis, TC
PROCEEDINGS OF THE SIXTH INTERNATIONAL COLLOQUIUM ON DIFFERENTIAL EQUATIONS, 1996, : 345 - 352
[22] An existence result for quasiequilibrium problems in separable Banach spaces
Castellani, M.
Giuli, M.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 425 (01) : 85 - 95
[23] On differential properties of mappings into a Banach space
A. V. Bondar’
Ukrainian Mathematical Journal, 1997, 49 (4) : 550 - 560
[24] Regularized Trace for Operators on a Separable Banach Space
Gul, Erdal
Gill, Tepper L.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (04)
[25] Regularized Trace for Operators on a Separable Banach Space
Erdal Gül
Tepper L. Gill
Mediterranean Journal of Mathematics, 2022, 19
[26] Coanalytic families of norms on a separable Banach space
Bossard, B
ILLINOIS JOURNAL OF MATHEMATICS, 1996, 40 (02) : 162 - 181
[27] PROBLEM OF BOLZA IN A SEPARABLE BANACH-SPACE
THIBAULT, L
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1976, 282 (22): : 1303 - 1306
[28] Integral geometric measure in separable Banach space
Bouafia, Philippe
De Pauw, T.
MATHEMATISCHE ANNALEN, 2015, 363 (1-2) : 269 - 304
[29] Integral geometric measure in separable Banach space
Philippe Bouafia
Thierry De Pauw
Mathematische Annalen, 2015, 363 : 269 - 304
[30] BORNOLOGICAL TOPOLOGY ON SPACE OF HOLOMORPHIC MAPPINGS ON A BANACH SPACE
ARON, RM
MATHEMATISCHE ANNALEN, 1973, 202 (04) : 265 - 272

← 1 2 3 4 5 →