Metric horseshoes

被引：40

作者：

Yang, XS ^{[1
]}

机构：

[1] Chongqing Univ, Inst Nonlinear Syst, Fac Elect Engn, Chongqing 400065, Peoples R China

[2] Xiamen Univ, Ctr Syst & Control, Xiamen 361005, Peoples R China

[3] Xiamen Univ, Dept Automat, Xiamen 361005, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2004年 / 20卷 / 05期

关键词：

D O I：

10.1016/j.chaos.2003.09.035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper a framework for metric horseshoe theory is developed to provide a criterion on the existence of horseshoes in maps with intension to offer a potential approach to study chaos in concrete systems via computer computations and simulations. (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：1149 / 1156

页数：8

共 10 条

[1] Chaos in the Hodgkin-Huxley Model [J].

Guckenheimer, John ;

Oliva, Ricardo A. .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2002, 1 (01) :105-114

[2] A chaos lemma [J].

Kennedy, J ;

Koçak, S ;

Yorke, JA .

AMERICAN MATHEMATICAL MONTHLY, 2001, 108 (05) :411-423

[3] Topological horseshoes [J].

Kennedy, J ;

Yorke, JA .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (06) :2513-2530

[4] CHAOS IN THE LORENZ EQUATIONS - A COMPUTER-ASSISTED PROOF [J].

MISCHAIKOW, K ;

MROZEK, M .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 32 (01) :66-72

[5] Topological invariants, multivalued maps and computer assisted proofs in dynamics [J].

Mrozek, M .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1996, 32 (04) :83-104

[6]

Wiggins S, 1990, INTRO APPL NONLINEAR, DOI 10.1007/b97481

[7] Horseshoes in piecewise continuous maps [J].

Yang, XS ;

Tang, Y .

CHAOS SOLITONS & FRACTALS, 2004, 19 (04) :841-845

[8] A new proof for existence of horseshoe in the Rossler system [J].

Yang, XS ;

Yu, YG ;

Zhang, SC .

CHAOS SOLITONS & FRACTALS, 2003, 18 (02) :223-227

[9]

YANG XS, IN PRESS INT J BIFUR

[10] Computer assisted proof of chaos in the Rossler equations and in the Henon map [J].

Zgliczynski, P .

NONLINEARITY, 1997, 10 (01) :243-252

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