2002/10/31 by Dmitry Kleinbock · 1 citation
Mathematics · #math.NT #math.DS #msc:11J83
published as GAFA 13 (2003), 437-466 · 26 pages. To appear in Geom. Funct. Anal. Several misprints corrected
arxiv created 2003/04/03 · arxiv updated 2009/11/30
It is known that the properties of almost all points of Rn being not very well (multiplicatively) approximable are inherited by nondegenerate in Rn (read: not contained in a proper affine subspace) smooth submanifolds. In this paper we consider submanifolds which are contained in proper affine subspaces, and prove that the aforementioned diophantine properties pass from a subspace to its nondegenerate submanifold. The proofs are based on a correspondence between multidimensional diophantine approximation and dynamics of lattices in Euclidean spaces.