Atratores globais para ações de semigrupos

Abstract

In this work, we introduce the concept of global attractor for semigroup actions on metric spaces. Initially, we study the theory of global attractor for semidynamical systems and then we extend all results for semigroup actions. We consider asymptotically compact semigroup actions, which have compact and invariant ?-limit sets, contributing to the study of the global attractor. We present necessary and sufficient conditions for the existence of the global attractor for semigroup actions and its characterization by ?-limit sets. To complete this work, we define the concepts of prolongation and prolongational limit set for semigroup action to introduce the concept of global uniform attracting set for semigroup actions and we present a relation between the notions of global attractor and global uniform attracting set