On the space of ergodic invariant measures of unipotent flows

Shahar Mozes, Nimish Shah

Research output: Contribution to journalArticlepeer-review

76 Scopus citations

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.

Original languageAmerican English
Pages (from-to)149-159
Number of pages11
JournalErgodic Theory and Dynamical Systems
Volume15
Issue number1
DOIs
StatePublished - Feb 1995

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