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Hadda Hmili; Isabelle Liousse
Dynamique des échanges d’intervalles des groupes de Higman-Thompson $V_{r,m}$
(Dynamics of affine interval transformations of Higman-Thompson groups $V_{r,m}$)
Annales de l'institut Fourier, 64 no. 4 (2014), p. 1477-1491, doi: 10.5802/aif.2887
Article PDF | Reviews MR 3329670 | Zbl 06387314
Class. Math.: 37E05, 37C85, 20F05
Keywords: Affine interval exchange transformations, groups, periodic orbits, distortion elements

Résumé - 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.

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