Abstract
Let be a symmetric space of noncompact type, and let be a lattice in the isometry group of . We study the distribution of orbits of acting on the symmetric space and its geometric boundary , generalizing the main equidistribution result of Margulis's thesis [M, Theorem 6] to higher-rank symmetric spaces. More precisely, for any and , we investigate the distribution of the set in . It is proved, in particular, that the orbits of in the Furstenberg boundary are equidistributed and that the orbits of in are equidistributed in “sectors” defined with respect to a Cartan decomposition. Our main tools are the strong wavefront lemma and the equidistribution of solvable flows on homogeneous spaces, which we obtain using Shah's result [S, Corollary 1.2] based on Ratner's measure-classification theorem [R1, Theorem 1]
Citation
Alexander Gorodnik. Hee Oh. "Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary." Duke Math. J. 139 (3) 483 - 525, 15 September 2007. https://doi.org/10.1215/S0012-7094-07-13933-4
Information