Dynamique des échanges d’intervalles des groupes de Higman-Thompson V_{r,m}

Abstract

In this paper, we study the dynamics of affine interval exchange transformations, whose slopes are integer powers of the same integer m, and whose cuts and their images are rational. We prove that such a map has very simple dynamics: all its orbits are proper and it has at least one periodic orbit or periodic cycle. As a corollary, we obtain that a distortion element of the Higman-Thompson group V r,m is of finite order.