Dynamics of isometries
Anders Karlsson, Kungliga tekniska högskolan, Stockholm, Sweden
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.