Distortion elements for surface homeomorphisms

Emmanuel Militon (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Let S be a compact orientable surface and f be an element of the group Homeo_{0}(S) of homeomorphisms of S isotopic to the identity. Denote by F a lift of f to the universal cover of S. In this article, the following result is proved: if there exists a fundamental domain D of the universal cover of S such that the sequence (d_{n}log(d_{n})/n) converges to 0 where d_{n} is the diameter of F^{n}(D), then the homeomorphism f is a distortion element of the group Homeo_{0}(S).

Domaines: Systèmes dynamiques [math.DS]

Emmanuel Militon. Distortion elements for surface homeomorphisms. Geometry and Topology, 2014, 18 (1), pp.521-614. ⟨hal-00713497v3⟩