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On the space of ergodic invariant measures of unipotent flows

Published online by Cambridge University Press:  19 September 2008

Shahar Mozes  and
Nimish Shah
Shahar Mozes
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
Nimish Shah
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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Abstract

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 1 , February 1995 , pp. 149 - 159
Copyright
Copyright © Cambridge University Press 1995

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