Dynamics of out(F-n) on the boundary of outer space

In this paper, we study the dynamics of the action of Out(F-n) on the bound ary partial derivative CVn of outer space: we describe a proper closed Out( F-n)-invariant subset F-n of partial derivative CVn such that Out(F-n) acts properly discontinuously on the complementary open set. Moreover, we prove that there is precisely one minimal non-empty closed invariant subset M-n in F-n. This set M-n is the closure of the Out(F-n)-orbit of any simplicial action lying in F-n. We also prove that M-n,, contains every action having at most n - 1 ergodic measures. This makes us suspect that M-n = F-n. Thus F-n would be the limit set of Out(F-n), the complement of F-n being its se t of discontinuity. (C) 2000 Editions scientifiques et medicales Elsevier S AS.