Fatou-Julia dichotomy of matrix-valued polynomials

Abstract

This article gives a precise description of the Fatou sets and Julia sets of matrix-valued polynomials in M(2,C) in terms of the corresponding polynomials in C. A normality criterion given by Aladro Krantz ([1]) plays a crucial role in proving this result. Further, we construct Green functions and Bottcher-type functions for these matrix-valued polynomials.