Date:	Tue, November 4, 2014
Time:	14:15
Place:	Research I Seminar Room

Abstract: Nekrashevich's approach to computation and understanding of iterated monodromy groups (IMGs) of polynomials is based on existence of an invariant star-like tree centered at infinity (called an invariant spider). Nekrashevych managed to describe a special class of automata, the kneading automata, such that the IMG of every post-critically finite polynomial is generated by an automaton in the class.

There is no known class of such automata for the rational case. Bonk and Meyer (and others) studied dynamical properties of a certain subclass of post-critically finite branched covering maps called expanding Thurston maps. Using their result we will outline a proof of existence of an invariant star-like tree for expanding Thurston maps which have a periodic critical point. This is the first step towards description of the iterated monodromy group of expanding Thurston maps.