In this paper, we study the action of non abelian group G generated by affine homotheties on R^n. We prove that G satisfies one of the following properties: (i) there exist a subgroup F_{ G} of R\{ 0} containing 0 in its closure, a G-invariant affine subspace E_{ G} of R^n and a in E_{ G} such that for every x in R^n the closure of the orbit G(x) is equal to F_{ G} .(x - a) +E_{ G}. In particular, G(x) is dense in E_{ G} for every x in E_{ G} and every orbit of U = R^n\E_{ G} is minimal in U. (ii) there exists a closed subgroup H_{ G} of R^n and a in R^n such that for every x in R^n, the closure of the orbit G(x) is equal to the union of (x + H_{ G}) and (-x + a + H_{ G}).
Categories: math.DS