Observing the symmetry of attractors

被引：4

作者：

Schenker, JH ^{[1
]}

Swift, JW ^{[1
]}

机构：

[1] No Arizona Univ, Dept Math, Flagstaff, AZ 86011 USA

来源：

PHYSICA D | 1998年 / 114卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

symmetric dynamical systems; bifurcation theory; coupled oscillators;

D O I：

10.1016/S0167-2789(97)00191-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and have been considered untrustworthy. We find conditions under which an equivariant projection generically shows the correct symmetry of the attractor. Copyright (C) 1998 Elsevier Science B.V.

引用

页码：315 / 337

页数：23

共 16 条

[1] RIDDLED BASINS [J].

Alexander, J. C. ;

Yorke, James A. ;

You, Zhiping ;

Kan, I. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1992, 2 (04) :795-813

[2]

[Anonymous], 1976, GRADUATE TEXTS MATH

[3] Attractors stuck on to invariant subspaces [J].

Ashwin, P .

PHYSICS LETTERS A, 1995, 209 (5-6) :338-344

[4] Detection of symmetry of attractors from observations .1. Theory [J].

Ashwin, P ;

Nicol, M .

PHYSICA D, 1997, 100 (1-2) :58-70

[5] DETECTING THE SYMMETRY OF ATTRACTORS [J].

BARANY, E ;

DELLNITZ, M ;

GOLUBITSKY, M .

PHYSICA D, 1993, 67 (1-3) :66-87

[6] SYMMETRY-INCREASING BIFURCATION OF CHAOTIC ATTRACTORS [J].

CHOSSAT, P ;

GOLUBITSKY, M .

PHYSICA D, 1988, 32 (03) :423-436

[7] HEXAPODAL GAITS AND COUPLED NONLINEAR OSCILLATOR MODELS [J].

COLLINS, JJ ;

STEWART, I .

BIOLOGICAL CYBERNETICS, 1993, 68 (04) :287-298

[8] ADMISSIBLE SYMMETRY INCREASING BIFURCATIONS [J].

DELLNITZ, M ;

HEINRICH, C .

NONLINEARITY, 1995, 8 (06) :1039-1066

[9]

DELLNITZ M, 1992, INT S NUM M, V104, P99

[10] SYMMETRY DETECTIVES FOR SBR ATTRACTORS [J].

GOLUBITSKY, M ;

NICOL, M .

NONLINEARITY, 1995, 8 (06) :1027-1037

← 1 2 →