Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
  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. 
Bas Lemmens, Brian Lins, Roger Nussbaum, and Marten Wortel
math.DS math.FA math.MG