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2005 On the dynamics of isometries
Anders Karlsson
Geom. Topol. 9(4): 2359-2394 (2005). DOI: 10.2140/gt.2005.9.2359

Abstract

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 Teichmüller 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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Anders Karlsson. "On the dynamics of isometries." Geom. Topol. 9 (4) 2359 - 2394, 2005. https://doi.org/10.2140/gt.2005.9.2359

Information

Received: 12 March 2005; Accepted: 16 December 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1120.53026
MathSciNet: MR2209375
Digital Object Identifier: 10.2140/gt.2005.9.2359

Subjects:
Primary: ‎37B05‎, 53C24
Secondary: 22F50, 32H50

Rights: Copyright © 2005 Mathematical Sciences Publishers

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