UNSPECIFIED (1994) TRANSITIVITY OF ORBITS OF MAPS SYMMETRICAL UNDER COMPACT LIE-GROUPS. CHAOS SOLITONS & FRACTALS, 4 (5). pp. 621-634. ISSN 0960-0779

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Abstract

We study the following idealised case of a map equivariant under a compact Lie group: let GAMMA be a connected compact Lie group and f: I x M to itself be continuous map with I a compact metric space and M a homogeneous GAMMA-space. Suppose f is equivariant under an orthogonal action of GAMMA on M. By assuming that on the orbit space I the map f is chaotic in the sense that it is a mixing (sub)shift, we show that generically f has orbits which are topologically transitive in their own group orbit. We relate this to some results from the ergodic theory of cocycles.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	CHAOS SOLITONS & FRACTALS
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
ISSN:	0960-0779
Date:	May 1994
Volume:	4
Number:	5
Number of Pages:	14
Page Range:	pp. 621-634
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20544

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