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On the dynamics of isometries
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2005 (English)In: Geometry and Topology, ISSN 1465-3060, E-ISSN 1364-0380, Vol. 9, 2359-2394 p.Article in journal (Refereed) Published
Abstract [en]

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 Teichmuller 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.

Place, publisher, year, edition, pages
2005. Vol. 9, 2359-2394 p.
Keyword [en]
metric spaces, isometries, nonpositive curvature, Kobayashi metric, random walk, pseudoconvex domains, poisson formula, boundary, spaces, theorem, maps
URN: urn:nbn:se:kth:diva-15281ISI: 000234226600002ScopusID: 2-s2.0-29344448635OAI: diva2:333322
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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