Complex Analysis, Dynamics and Geometry Seminar

We consider the parameter space Per(p, 0) of cubic polynomials with a marked critical point that is constrained to be periodic of period p. The complement of the connectedness locus consists of a finite set of punctured disks, referred to as escape regions. In this talk, I will describe some of the work of DeMarco and Pilgrim, who show that discrete structures known as pictographs can be used to partially, though not completely, distinguish escape regions up to topological conjugacy. In the latter part of the talk, I will discuss ongoing efforts to generalize the work of Blanchard, Devaney, and Keen connecting the monodromy of escape regions to automorphisms of the shift. Speaker(s): Danny Stoll (U(M))