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Ergodic elements for actions of Lie groups

Published online by Cambridge University Press:  19 September 2008

K. Robert Gutschera
K. Robert Gutschera
Affiliation:
Department of Mathematics, Wellesley College, Wellesley, MA 02181, USA (e-mail: krg@olaf.wellesley.edu)
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Abstract

Given a connected Lie group G acting ergodically on a space S with finite invariant measure, one can ask when G will contain single elements (or one-parameter subgroups) that still act ergodically. For a compact simple group or the isometry group of the plane, or any group projecting onto such groups, an ergodic action may have no ergodic elements, but for any other connected Lie group ergodic elements will exist. The proof uses the unitary representation theory of Lie groups and Lie group structure theory.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 703 - 717
Copyright
Copyright © Cambridge University Press 1996

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