Observing the symmetry of attractors

Jeffrey H. Schenker; James W. Swift

doi:10.1016/S0167-2789(97)00191-7

Observing the symmetry of attractors

Jeffrey H. Schenker, James W. Swift

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	315-337
Number of pages	23
Journal	Physica D: Nonlinear Phenomena
Volume	114
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(97)00191-7
State	Published - 1998

Keywords

Bifurcation theory
Coupled oscillators
Symmetric dynamical systems

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/S0167-2789(97)00191-7

Cite this

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title = "Observing the symmetry of attractors",

abstract = "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.",

keywords = "Bifurcation theory, Coupled oscillators, Symmetric dynamical systems",

author = "Schenker, {Jeffrey H.} and Swift, {James W.}",

note = "Funding Information: This research was supported by the NSF through the Research Experience for Undergraduates (REU) program. We would like to thank Peter Ashwin, Matt Nicol, Mike Field, Mike Falk, Michael Dellnitz, John Hagood, Farhad Jafari and Steve Fromm for helpful discussions.",

year = "1998",

doi = "10.1016/S0167-2789(97)00191-7",

language = "English (US)",

volume = "114",

pages = "315--337",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier B.V.",

number = "3-4",

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TY - JOUR

T1 - Observing the symmetry of attractors

AU - Schenker, Jeffrey H.

AU - Swift, James W.

N1 - Funding Information: This research was supported by the NSF through the Research Experience for Undergraduates (REU) program. We would like to thank Peter Ashwin, Matt Nicol, Mike Field, Mike Falk, Michael Dellnitz, John Hagood, Farhad Jafari and Steve Fromm for helpful discussions.

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - Bifurcation theory

KW - Coupled oscillators

KW - Symmetric dynamical systems

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U2 - 10.1016/S0167-2789(97)00191-7

DO - 10.1016/S0167-2789(97)00191-7

M3 - Article

AN - SCOPUS:4243542029

SN - 0167-2789

VL - 114

SP - 315

EP - 337

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -

Observing the symmetry of attractors

Abstract

Keywords

ASJC Scopus subject areas

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