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TRANSITIVITY OF ORBITS OF MAPS SYMMETRICAL UNDER COMPACT LIE-GROUPS
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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 | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | CHAOS SOLITONS & FRACTALS | ||||
Publisher: | PERGAMON-ELSEVIER SCIENCE LTD | ||||
ISSN: | 0960-0779 | ||||
Official Date: | May 1994 | ||||
Dates: |
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Volume: | 4 | ||||
Number: | 5 | ||||
Number of Pages: | 14 | ||||
Page Range: | pp. 621-634 | ||||
Publication Status: | Published |
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