%0 Journal Article
%T Khinchin theorem for integral points on quadratic varieties
%A Alexander Gorodnik
%A Nimish A. Shah
%J Mathematics
%D 2008
%I arXiv
%X We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.
%U http://arxiv.org/abs/0804.3530v1