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Symmetric omega-limit sets for smooth Gamma-equivariant dynamical systems with Gamma0 Abelian

Melbourne, Ian and Stewart, Ian N. (1997) Symmetric omega-limit sets for smooth Gamma-equivariant dynamical systems with Gamma0 Abelian Nonlinearity, 10. pp. 1551-1567.

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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 Gamma0 is Abelian and show that under fairly mild assumptions on the dynamics, it is typically the case that the symmetry of an -limit set contains the continuous symmetries Gamma0. Here, typicality is interpreted in both a topological and probabilistic sense (genericity and prevalence).

Item Type: Article
Additional Information: This is a pre-copy-editing, author-prepared, peer-reviewed PDF of an article published in Nonlinearity, 10, 1551-1567. © 1997 IOP Publishing Ltd. Click here to visit the publisher's website.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1447

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