Topological dynamics

Abstract

This chapter is dedicated to the study of semidynamical systems generated by generalized ordinary differential equations (ODEs). Besides the existence of a local semidynamical system, it shows the existence of an associated impulsive semidynamical system. The chapter concerns the existence of a local semidynamical system generated by the nonautonomous generalized ODE. It investigates properties of the impulsive generalized ODE associated with the initial value problem. The chapter presents a version of LaSalle’s invariance principle in the context of generalized ODEs. It provides the concept of a limit set on impulsive semidynamical systems in the frame of generalized ODEs, and also presents the concepts of minimality and recurrence.