Explorando os teoremas de linearização de Philip-Hartman através de exemplos e aplicações: Caso discreto

Caso discreto

Abstract

This work was written to students of mathematics, physics, biology and engineering. In mathematics, the nonlinear term basically means ``difficult to analyze''. Since linear systems are easier to analyze,
a key way to understand nonlinear systems is to find out where and when they can be well-approximated by linear systems. In this sense to help,
among others, we have the linearization theorems of Hartman \cite{Hartman, Hartman2}. In this work, we will introduce the notion of discrete dynamic systems and dynamic conjugation. Through some constructed examples and a bibliographical review of some famous examples in the field, we will analyze the importance and limitations of Hartman's theorems. Finally, we will study an application of Hénon, locally, by way of the Hartman's linearization.