Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem

Abstract

The goal of this paper is proving the existence and then localizing global fixed points for nilpotent groups generated by homeomorphisms of the plane satisfying a certain Lipschitz condition. The condition is inspired in a classical result of Bonatti for commuting diffeomorphisms of the 2-sphere and in particular it is satisfied by diffeomorphisms, not necessarily of class $C^1$, whose linear part at every point is uniformly close to the identity. In this same setting we prove a version of the Cartwright-Littlewood theorem, obtaining fixed points in any continuum preserved by a nilpotent action.

30 pages, 2 figures

References in corpus (1)

• Fixed points of nilpotent actions on ${\mathbb{S}}^2$

Cited by in corpus (1)

• Fixed points of nilpotent actions on ${\mathbb{S}}^2$