Composition arithmetic for locally one-to-one entire mappings

TL;DR

This paper explores the factorization properties of entire functions with non-vanishing derivatives, demonstrating that this family includes prime functions and possesses two distinct fractal representations.

Contribution

It introduces a factorization framework for entire functions with non-vanishing derivatives and proves the existence of prime functions within this family.

Findings

The family of entire functions with non-vanishing derivatives contains prime functions.

This family admits two non-degenerate fractal representations.

Abstract

This paper describes a part of the factorization theory of the family of all the entire functions with non vanishing derivatives. In particular it proves that this family of mappings contains primes. This assures that this family of entire functions has two non degenerate fractal representations.