Rigorous Numerics and Polynomial Skew Products of C²
by
Suzanne Hruska
Indiana University

Our goal is to develop and use rigorous computer investigations to study the dynamics of polynomial skew products of C²; i.e., maps of the form f(z, w) = (p(z), q(z, w)), where p and q are polynomials of the same degree d ≥ 2. The skew products we are most interested in studying are those maps which are Axiom A. Such maps have the "simplest" chaotic dynamics, and stability under small perturbation, thus are amenable to computer investigation. In this talk, we will describe a new class of skew products with interesting dynamics, and sketch how we have proven using rigorous computer techniques that sample maps from this class are Axiom A. This leads us to conjecture that all (or nearly all) maps in this class are Axiom A.

Date received: February 23, 2006