On the struture of homeomorphims of the open annulus

Lucien Guillou (1)

1 IF - Institut Fourier

Let $h$ be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that $h$ admits a $h$-invariant dense open set $O$ on which it is conjugate to a translation and we study the action of $h$ on the compactly connected components of the closed and without interior set ${\bf R}^2 \setminus O$.

Domaines: Systèmes dynamiques [math.DS]

Lucien Guillou. On the struture of homeomorphims of the open annulus. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2011, 20 (2), pp.367-378. ⟨hal-00390434⟩