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

Lemmens, Bas, Lins, Brian, Nussbaum, Roger, Wortel, Marten (2018) Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces. Journal d'Analyse Mathematique, 134 (2). pp. 671-718. ISSN 0021-7670. E-ISSN 1565-8538. (doi:10.1007/s11854-018-0022-2)

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https://doi.org/10.1007/s11854-018-0022-2

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.

Item Type: Article
DOI/Identification number: 10.1007/s11854-018-0022-2
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA440 Geometry
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Bas Lemmens
Date Deposited: 09 Oct 2014 10:40 UTC
Last Modified: 15 Jan 2020 15:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/43236 (The current URI for this page, for reference purposes)
Lemmens, Bas: https://orcid.org/0000-0001-6713-7683
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