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arXiv · 1410.1056

Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces

Bas Lemmens·Brian Lins·Roger Nussbaum·Marten Wortel
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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.

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Bas Lemmens, Brian Lins, Roger Nussbaum, Marten Wortel. 2016-06-14. Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces. https://arxiv.org/abs/1410.1056

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