Let V be an affine symmetric variety defined over Q. We compute the
asymptotic distribution of the angular components of the integral points in V.
This distribution is described by a family of invariant measures concentrated
on the Satake boundary of V. In the course of the proof, we describe the
structure of the Satake compactifications for general affine symmetic varieties
and compute the asymptotic of the volumes of norm balls.Comment: to appear in Amer. J. Mat
