Lemmens, BasWortel, MartenLins, BrianNussbaum, Roger2018-04-112018-04-112018Lemmens, B. et al. 2018. Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces. Journal d'analyse mathematique, 134(2):671-718. [https://doi.org/10.1007/s11854-018-0022-2]0021-76701565-8538 (Online)http://hdl.handle.net/10394/26677https://doi.org/10.1007/s11854-018-0022-2https://link.springer.com/article/10.1007/s11854-018-0022-2We 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 which 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 mappingsenArticle