Texas A&M University, Department of
Mathematics, 216 Milner Hall, 23rd of February 2005, 3:00-3:50
Groups and Dynamics Seminar
(joint session with Mathematical
Physics and Harmonic Analysis Seminar)
Iterated monodromy
groups, Schreier graphs and limit spaces
Volodymyr Nekrashevych of International
University Bremen, Germany
Iterated monodromy groups are naturally associated to (branched)
self-coverings of topological spaces (for instance, to the rational
functions acting on the Riemann sphere). We will show how iterated
monodromy groups encode information about the dynamics of the
self-covering. In particular, in many cases the Julia set of the
self-covering can be reconstructed from the associated iterated
monodromy group. This is done using the notion of a limit space of a
group acting on a rooted tree. The limit space is approximated by
Schreier graphs of the group and usually has a fractal shape. We will
give different examples of iterated monodromy groups and their limit
spaces.