Polynomial-time Computability of the Julia Set for Polynomial Skew Products of Two Complex Variables

Dr. Suzanne Boyd
Associate Professor
University of Wisconsin-Milwaukee

Ingrained in the modern study of dynamical systems is the use of computer experiments for revelation and illustration. In this talk, I will explain a polynomial-time computer algorithm for approximating the Julia set of a polynomial skew product of two complex variables. I will begin by defining the involved terms, including computability, Julia set, and polynomial skew product. This work is joint with Christian Wolf. It relies on some my previous work on designing and implementing rigorous computer algorithms to confirm results of the experimental observations on the dynamics of polynomial maps of two complex variables, including polynomial skew products. These algorithms are designed to locate a neighborhood of the chain recurrent set, build a model of the dynamics of the map on this set, and attempt to determine hyperbolicity (or Axiom A) of the map on its chain recurrent set.