Dynamics of isometries
Anders Karlsson, Kungliga tekniska högskolan, Stockholm, Sweden
Abstract
We provide an analysis of the dynamics of groups of isometries
of metric
spaces.
Certain subsets, called stars, of a given boundary at infinity play a
fundamental role and give rise to an incidence geometry (related to Tits
geometries, face lattices, curve complexes, etc.). The stars can be
completely identified for the standard boundaries of CAT(0)-spaces, Gromov
hyperbolic spaces, Hilbert geometries, certain pseudoconvex domains, and
partially determined for Thurston's boundary of Teichmuller spaces. A
metric Furstenberg lemma as well as some new results and aspects of
boundary theory of random walks, groups acting on CAT(0)-spaces,
L2
cohomology, and dynamics of holomorphic maps will be discussed.