On Completely Invariant Julia Sets of Trascendental Semigroups

TL;DR

This paper introduces the concept of completely invariant Julia sets in transcendental semigroup dynamics and explores how classical results extend to this broader context.

Contribution

It defines the completely invariant Julia set for transcendental semigroups and investigates the extent of classical dynamics results in this new setting.

Findings

Definition of completely invariant Julia set for transcendental semigroups

Analysis of classical dynamics results in the context of semigroup dynamics

Insights into invariance properties of Julia sets in semigroup theory

Abstract

In holomorphic semigroup dynamics, Julia set is in general backward invariant and so some fundamental results of classical complex dynamics can not be generalized to semigroup dynamics. In this paper, we define completely invariant Julia set of transcendental semigroup and we see how far the results of classical transcendental dynamics generalized to transcendental semigroup dynamics.