Pontos periódicos de funções afins por partes e o Teorema de Li e Yorke: uma introdução no Ensino médio

Abstract

In this paper, we discuss the concepts of fixed points and periodic points of a discrete dynamical system. More specifically, we use fundamental tools of Real Analysis, such as the Intermediate Value Theorem, to guarantee the existence of such points in a unidimensional dynamical system. We also present the Li and Yorke Theorem, which states that the existence of a periodic point of period 3 in a dynamical system guarantees the existence of periodic points of any period. The paper ends with an ”Activity Book” that addresses such content in the dynamics of affine functions and piecewise affine functions. This “Activity Book”, intended for high school students, contemplates the competences and skills proposed at CNCB (Common National Curriculum Base) and helps the teacher to work the contents proposed in an investigative and participatory way.