Alguns critérios de caoticidade de operadores em espaços de Fréchet

Abstract

In this work, we study some dynamical properties of continuous linear operators on Fréchet spaces, focusing on the concepts of hypercyclicity, chaoticity, and frequent hypercyclicity. We study important conditions and results that characterize hypercyclic operators, chaotic operators, and frequently hypercyclic operators, and we explore the Hypercyclicity Criterion, Kitai Criterion, Gethner–Shapiro Criterion, Chaoticity Criterion, and the Frequent Hypercyclicity Criterion. We study the relationship that these criteria have with other notions of chaos, especially topological transitivity, as well as the notions of mixing and weakly mixing. Furthermore, we present examples, in each one of these cases, to show that such criteria provide sufficient, but not necessary, conditions for determining each of these notions.