Uniqueness of Holomorphic Abel Functions at a Complex Fixed Point Pair

TL;DR

This paper establishes a simple criterion for the uniqueness of holomorphic Abel functions and demonstrates its application to Kneser's real analytic Abel function of the exponential.

Contribution

It introduces a new criterion for the uniqueness of holomorphic Abel functions and applies it to a well-known exponential Abel function.

Findings

The criterion effectively determines the uniqueness of holomorphic Abel functions.

Kneser's Abel function of the exponential satisfies the new uniqueness criterion.

Abstract

We give a simple uniqueness criterion (and some derived criteria) for holomorphic Abel functions and show that Kneser's real analytic Abel function of the exponential is subject to this criterion.