On the reduction to a subspace of stability properties of systems in metric spaces

Abstract

The objects studied are dynamical and semidynamical systems defined on arbitrary metric spaces. Sufficient conditions for stability and asymptotic stability (both local and global) of a compact invariant set are established, using the corresponding properties of the (semi-) dynamical systems induced on a (positively) invariant subset. © 1995 Fondazione Annali di Matematica Pura ed Applicata.