Um estudo sobre alguns tópicos em sistemas dinâmicos unidimensionais e aplicações ao cálculo de raízes de uma equação

Abstract

This work presents an introductory study on discrete one-dimensional dynamical systems. We approached the initial concepts for the study of dynamical systems, such as the notions of orbits, fixed point and period point. In addition, we study the dy- namical behavior of an one-parameter family of quadratic functions that, surprisingly, presents very different behaviors for different parameters. We finish our work with a small discussion about the root calculation of an equation through iterations, in particular Newton’s method is one of these methods.