Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
Dynamical Systems
2016-06-15 v4 Functional Analysis
Metric Geometry
Abstract
We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert's metric or Thompson's metric. We establish several Denjoy-Wolff type theorems that confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.
Keywords
Cite
@article{arxiv.1410.1056,
title = {Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces},
author = {Bas Lemmens and Brian Lins and Roger Nussbaum and Marten Wortel},
journal= {arXiv preprint arXiv:1410.1056},
year = {2016}
}
Comments
41 pages. To appear in J. Anal. Math. Corrected some typos