Dispersividade e recursividade para ações de semigrupos

Abstract

The recursive and dispersive concepts for dynamical systems in metric spaces are related to Poisson stability, non-wandering points, Poisson instability and dispersive points. The present thesis extends these concepts to semigroup actions on admissible spaces. We present the concepts of prolongation, prolongational limit sets, Poisson stability, non-wandering points, Poisson instability and dispersive points for semigroups actions. Prove the main property of a non-dispersive point, i.e., the point is non-dispersive if, and only if, this point belongs to the whole prolongational limit and show conditions for which the action is dispersive if, and only if, for every point of the topological space, the prolongation of this point is equal to its orbit and there are not almost periodic points. We also present some applications to control systems and fiber bundles