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

  • Dmitry Kleinbock

    Brandeis University, Waltham, United States
  • George Tomanov

    Université Claude Bernard Lyon 1, Villeurbanne, France

Abstract

The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and -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 ) are generalized to the -arithmetic setting.

Cite this article

Dmitry Kleinbock, George Tomanov, Flows on -arithmetic homogeneous spaces and applications to metric Diophantine approximation. Comment. Math. Helv. 82 (2007), no. 3, pp. 519–581

DOI 10.4171/CMH/102