The dynamics of semigroups of transcendental entire functions I

TL;DR

This paper explores the complex dynamics of semigroups formed by transcendental entire functions, extending classical iteration results and analyzing special cases like conjugate, Abelian, and wandering domains.

Contribution

It extends Fatou-Julia theory to transcendental semigroups and investigates their dynamics, including conjugate, Abelian, and wandering domains.

Findings

Extended classical dynamics results to semigroups

Analyzed conjugate and Abelian semigroups dynamics

Studied wandering and Baker domains in semigroups

Abstract

We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups, Abelian transcendental semigroups and wandering and Baker domains of transcendental semigroups.