One-end finitely presented groups acting on the circle

Dmitry A. Filimonov (1) , Victor A. Kleptsyn (2)

1 Higher School of Economics
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study possible one-end finitely presented subgroups of Diff(+)(omega)(S-1), acting without finite orbits. Our main result, theorem 1, establishes that any such action possesses the so-called property (star), that allows one to make distortion-controlled expansion and is thus sufficient to conclude that the action is Lebesgue-ergodic. We also propose a path towards full characterization of such actions (conjectures 3-5).

Mots clés: group actions; circle diffeomorphisms; dynamical systems

Domaines: Systèmes dynamiques [math.DS]

Dmitry A. Filimonov, Victor A. Kleptsyn. One-end finitely presented groups acting on the circle. Nonlinearity, 2014, 27 (6), pp.1205-1223. ⟨10.1088/0951-7715/27/6/1205⟩. ⟨hal-01022021⟩