Stability of Blaschke products under forward iteration

TL;DR

This paper studies the behavior of Blaschke products under forward iteration, showing that certain classes remain stable, which advances understanding in complex dynamics and iteration theory.

Contribution

It proves the stability of indestructible and maximal Blaschke products under forward iteration, extending their known properties in complex dynamics.

Findings

Indestructible Blaschke products are stable under forward iteration.

Maximal Blaschke products remain stable when iterated forward.

The results contribute to the understanding of iteration stability in complex dynamics.

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.