An underlying theory of multifunctions in discrete-time set-valued dynamical systems

We study the asymptotic behaviour of discrete time set-valued dynamical systems defined by difference inclusions. Notions as limit sets, invariant or attractors sets are defined in terms of set-valued analysis and relations with different concepts of stable set (in the Lyapunov sense) are established. In this brief paper, we present applications of set-valued analysis to the dynamical system theory and provide a foundational theory in terms of stability analysis.