Numerical Range and the Dynamics of a Rational Function

TL;DR

This paper proposes a new approach to studying the dynamics of rational functions by associating simple elements to complex facts, aiming to simplify and enhance understanding of their behavior.

Contribution

It introduces an alternative method for analyzing rational map dynamics, focusing on the association of simple elements to complex phenomena.

Findings

New framework for rational map dynamics

Potential simplification of complex behavior analysis

Foundation for further research in dynamical systems

Abstract

Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.