Stability of Blaschke products under forward iteration

Abstract

Forward iteration of holomorphic self-maps generalizes the iteration of a single function in a natural way. This framework arises in complex dynamics, for instance in the study of wandering domains and in seeking suitable extensions of the Denjoy-Wolff theorem. Here, we consider forward iteration of Blaschke products. We prove that the classes of indestructible and maximal Blaschke products are stable under forward iteration.

to appear in Bull. Lond. Math. Soc