2010/09/27 by Adlene Ayadi, Ayadi, Adlene, Yahya N'Dao +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1009.5356
arxiv created 2010/10/07 · arxiv updated 2010/10/08
In this paper, we study the action of non abelian group G generated by affine homotheties on Rn. We prove that G satisfies one of the following properties: (i) there exist a subgroup FG of R\0 containing 0 in its closure, a G-invariant affine subspace EG of Rn and a in EG such that for every x in Rn the closure of the orbit G(x) is equal to FG .(x - a) +EG. In particular, G(x) is dense in EG for every x in EG and every orbit of U = Rn\EG is minimal in U. (ii) there exists a closed subgroup HG of Rn and a in Rn such that for every x in Rn, the closure of the orbit G(x) is equal to the union of (x + HG) and (-x + a + HG).