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) (KAR id:43236)

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Official URL: 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:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Funders:	Engineering and Physical Sciences Research Council (https://ror.org/0439y7842)
Depositing User:	Bas Lemmens
Date Deposited:	09 Oct 2014 10:40 UTC
Last Modified:	12 Jul 2022 10:40 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/43236 (The current URI for this page, for reference purposes)

University of Kent Author Information

Lemmens, Bas.

Creator's ORCID:	https://orcid.org/0000-0001-6713-7683
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