TRANSITIVITY OF ORBITS OF MAPS SYMMETRICAL UNDER COMPACT LIE-GROUPS
UNSPECIFIED. (1994) TRANSITIVITY OF ORBITS OF MAPS SYMMETRICAL UNDER COMPACT LIE-GROUPS. CHAOS SOLITONS & FRACTALS, 4 (5). pp. 621-634. ISSN 0960-0779Full text not available from this repository.
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|
|Official Date:||May 1994|
|Number of Pages:||14|
|Page Range:||pp. 621-634|
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