Hausdorffization, monotone-light factorizations, and the global topology of polynomial shift loci
by
Kevin M. Pilgrim
Indiana University
Coauthors: Laura DeMarco, UIC

Iterating a complex polynomial gives a dynamical system on the complex plane. The space of all such polynomials of a fixed degree d ≥ 2, modulo complex coordinate changes, contains a distinguished shift locus S_d consisting of maps all of whose critical points escape under iteration. The global topology of S_d is quite complicated. We describe some general structural features of S_d. This is a first step in a program to classify the topological conjugacy classes of shift polynomials on their basins of infinity.

Date received: February 3, 2010