On the dynamics of isometries

Details On the dynamics of isometries On the dynamics of isometries

2005-12-29

arxiv.org/abs/math/0512638v1

Geom. Topol. 9(2005) 2359-2394

Mathematics

Metric Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper55.abs.html

Scientific paper

We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)-spaces, Gromov hyperbolic spaces, Hilbert geometries, certain pseudoconvex domains, and partially for Thurston's boundary of Teichmueller spaces. We present several rather general results concerning groups of isometries, as well as the proof of other more specific new theorems, for example concerning the existence of free nonabelian subgroups in CAT(0)-geometry, iteration of holomorphic maps, a metric Furstenberg lemma, random walks on groups, noncompactness of automorphism groups of convex cones, and boundary behaviour of Kobayashi's metric.

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