UNSPECIFIED (1997) Symmetric omega-limit sets for smooth Gamma-equivariant dynamical systems with Gamma(0) Abelian. NONLINEARITY, 10 (6). pp. 1551-1567. ISSN 0951-7715

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Abstract

The symmetry groups of attractors for smooth equivariant dynamical systems have been classified when the underlying group of symmetries Gamma is finite. The problems that arise when Gamma is compact but infinite are of a completely different nature. We investigate: the case when the connected component of the identity Gamma(0) is Abelian and show that under fairly mild assumptions on the dynamics, it is typically the case that the symmetry of an omega-limit set contains the continuous symmetries Gamma(0). Here, typicality is interpreted in both a topological and probabilistic sense (genericity and prevalence).

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	NONLINEARITY
Publisher:	IOP PUBLISHING LTD
ISSN:	0951-7715
Date:	November 1997
Volume:	10
Number:	6
Number of Pages:	17
Page Range:	pp. 1551-1567
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/16231

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