Lyapunov Stability and Attraction Under Equivariant Maps

Abstract

AbstractLetMandNbe admissible Hausdorff topological spaces endowed with admissible families of open coverings. Assume thatis a semigroup acting on bothMandN. In this paper we study the behavior of limit sets, prolongations, prolongational limit sets, attracting sets, attractors, and Lyapunov stable sets (all concepts deûned for the action of the semigroup) under equivariant maps and semiconjugations fromMtoN.