Flows on $S$-arithmetic homogeneous spaces and applications to metric Diophantine approximation

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75582The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and $p$-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock-Margulis (strong extremality of nondegenerate submanifolds of $\Bbb R^n$) are generalized to the $S$-arithmetic setting.56 pages; an earlier version is available as an MPI (Bonn) preprint, 2003Number TheoryDynamical Systems11J83; 37A13Flows on $S$-arithmetic homogeneous spaces and applications to metric Diophantine approximationtext