Primeness and dynamics of some classes of entire functions

TL;DR

This paper studies the primeness of certain entire functions and explores the dynamics of their periodic members, showing that such functions share the same Julia sets when permuted with transcendental entire functions.

Contribution

It introduces new results on the primeness of specific classes of entire functions and their dynamic behavior under permutation with transcendental functions.

Findings

Julia sets of permuted functions are identical

Periodic members exhibit specific dynamical properties

New criteria for primeness of entire functions

Abstract

In this paper we investigate the primeness of a class of entire functions and discuss the dynamics of a periodic member f of this class with respect to a transcendental entire function g that permutes with f. In particular we show that the Julia sets of f and g are identical.