Estabilidade estrutural e estatística das transformações expansoras

Abstract

In this work, we will discuss about the structural stability and the statistical stability of expanding maps. As an application of the Shadowing Lemma, we will prove that every C 1 expanding map is structurally stable, which means that all dynamics sufficiently close are topologically conjugated to it. Next, we will prove the existence and uniqueness of an invariant measure, absolutely continuous with respect to the Lebesgue measure. Finally, we will prove that the expanding map is statistically stable, that is, the unique ergodic measure absolutely continuous to Lebesgue varies continuously.