Complex Analysis, Dynamics and Geometry Seminar

The celebrated Nielsen-Thurston classification of surface homeomorphisms says that, up to isotopy, there are three types of homeomorphisms of a closed, connected surface: (1) finite order, (2) reducible, and (3) pseudo-Anosov. Of these three types, pseudo-Anosovs are the most intriguing to dynamicists, with connections to symbolic dynamics and flat geometry. In this talk we investigate a construction of generalized pseudo-Anosovs from interval maps, first introduced by de Carvalho. In particular, for a certain class of interval maps we give necessary and sufficient conditions for the construction to produce a true pseudo-Anosov, which may be recast in terms of the kneading data of the interval map. We also describe a bijection between such interval maps and the rationals in the open unit interval which captures the kneading data, and which seems to increase monotonically in the entropy of the interval map. Speaker(s): Ethan Farber (Boston College)