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Flows on Homogeneous Spaces: A New Look

Jonathan Brezin and Calvin C. Moore
American Journal of Mathematics
Vol. 103, No. 3 (Jun., 1981), pp. 571-613
DOI: 10.2307/2374105
Stable URL: http://www.jstor.org/stable/2374105
Page Count: 43
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Flows on Homogeneous Spaces: A New Look
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Abstract

We consider homogeneous spaces G/D where G is a Lie group and D is a closed subgroup with the property that G/D has a finite G invariant measure. If x(t) = exp(tX) is a one parameter group in G, it induces by left translations a one parameter group of measure preserving diffeomorphisms of G/D. The problem of determining necessary and sufficient conditions for such a flow to be ergodic and the problem of determining the spectral type of the infinitesimal generator of such a flow have a long history. In this paper we discuss solutions to these problems in their most general form.

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