Characterization of the hyperbolic step of parabolic functions

TL;DR

This paper introduces new intrinsic characterizations of the hyperbolic step for parabolic functions in complex dynamics, advancing understanding of their iterative behavior on hyperbolic domains.

Contribution

It offers novel intrinsic property-based characterizations of the hyperbolic step, improving upon previous results that depended on iterative behavior.

Findings

New intrinsic characterizations of the hyperbolic step

Enhanced understanding of parabolic functions in hyperbolic domains

Connections between intrinsic properties and iterative behavior

Abstract

A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that depend on the behaviour of the iterates of such function. In this work we provide new characterizations in terms of intrinsic properties of the function.