Ergodic Theory and Dynamical Systems

Research Article

On the space of ergodic invariant measures of unipotent flows

Shahar Mozesa1 and Nimish Shaha2

a1 Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

a2 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

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.

(Received April 26 1993)

Footnotes

† Sponsored in part by the Edmund Landau Center for research in Mathematical Analysis supported by the Minerva Foundation (Federal Republic of Germany).

‡ Research at MSRI supported by NSF grant DMS8505550.