Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem
Dynamical Systems
2018-11-01 v1
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 , 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.
Keywords
Cite
@article{arxiv.1306.0232,
title = {Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem},
author = {S. Firmo and J. Ribón and J. Velasco},
journal= {arXiv preprint arXiv:1306.0232},
year = {2018}
}
Comments
30 pages, 2 figures