Limit distributions of expanding translates of certain orbits on homogeneous spaces
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چکیده
Let L be a Lie group and A a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L and G---A = L. Let a~G be such that Ada is semisimple and not contained in a compact subgroup of Aut (Lie(G)). Consider the expanding horospherical subgroup of G associated to a defined as U + = {g~ G:a-"ga"~ e as n ~ oo}. Let f2 be a non-empty open subset of U § and nf-* ~ be any sequence. It is showed that u~=~a"'DA = L. A stronger measure theoretic formulation of this result is also obtained. Among other applications of the above result, we describe G-equivariant topological factors of L/A x G/P, where the real rank of G is greater than 1, P is a parabolic subgroup of G and G acts diagonally. We also describe equivariant topological factors of unipotent flows on finite volume homogeneous spaces of Lie groups.
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