Complex Analysis, Dynamics and Geometry Seminar

Discrete time dynamical systems can often be understood by studying their periodic orbits. By marking such a periodic orbit on an algebraic family of holomorphic functions, one obtains a branched cover whose geometry reflects the interactions between the various n-cycles arising in the family. We describe an algorithm to compute this branched cover for n-cycles under quadratic polynomials, along with partial results and generalizations to other families. Speaker(s): Danny Stoll (U(M))