UNSPECIFIED (1998) On symmetric attractors in reversible dynamical systems. In: Workshop on Time-Reversal Symmetry in Dynamical Systems, DEC 09-23, 1996, WARWICK, ENGLAND.

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Abstract

Let Gamma subset of O(n) be a finite group acting orthogonally on R ". We say that Gamma is a reversing symmetry group of a homeomorphism, diffeomorphism or flow f(t) : R " (bar right arrow) R " (t epsilon Z or t epsilon R) if Gamma has an index two subgroup <(Gamma)over bar> whose elements commute with f(t) and for all elements rho epsilon Gamma - <(Gamma)over bar> and all t, f(t) circle rho(x) = rho circle f(-t)(x). We give necessary group and representation theoretic conditions for subgroups of reversing symmetry groups to occur as symmetry groups of attractors (Lyapunov stable omega-limit sets). These conditions arise due to topological obstructions. In dimensions 1 and 2 we present a complete description of possible symmetry groups of asymptotically stable attractors for homeomorphisms and diffeomorphisms (these attractors cannot possess reversing symmetries). We also have a fairly complete description in the context of subgroups which contain reversing symmetries. For ail dimensions n we present complete results on the possible symmetry groups of connected asymptotically stable attractors. In addition, we summarize our results in the context of reversible equivariant flows, which are complete in dimensions 1 and 2 as well as for subgroups of <(Gamma)over bar> subset of O(n) in any dimension n. A survey of the corresponding results in the equivariant context is also given.

Item Type:	Conference Item (UNSPECIFIED)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	15 January 1998
Volume:	112
Number:	1-2
Number of Pages:	17
Page Range:	pp. 281-297
Publication Status:	Published
Title of Event:	Workshop on Time-Reversal Symmetry in Dynamical Systems
Location of Event:	WARWICK, ENGLAND
Date(s) of Event:	DEC 09-23, 1996
URI:	http://wrap.warwick.ac.uk/id/eprint/16061

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