On orbits of unipotent flows on homogeneous spaces

Dani, S. G. (1984) On orbits of unipotent flows on homogeneous spaces Ergodic Theory and Dynamical Systems, 4 (1). pp. 25-34. ISSN 0143-3857

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Related URL: http://dx.doi.org/10.1017/S0143385700002248


Let G be a connected Lie group and let Γ be a lattice in G (not necessarily co-compact). We show that if (ut) is a unipotent one-parameter subgroup of G then every ergodic invariant (locally finite) measure of the action of (ut) on G/Γ is finite. For 'arithmetic lattices' this was proved in [2]. The present generalization is obtained by studying the 'frequency of visiting compact subsets' for unbounded orbits of such flows in the special case where G is a connected semi-simple Lie group of R-rank 1 and Γ is any (not necessarily arithmetic) lattice in G.

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