Chain Recurrence in Graph Determined Hybrid Systems

Abstract

In this paper, we consider a family of dynamical systems on the same compact metric space. We then consider the dynamics given when the given flow shifts between these different flows at regular time intervals. We further require that shifts be allowed by a given directed graph. We then define a type of set, called a chain set, that exhibits many similar properties to chain transitive sets of flows. By considering the dynamics as a skew product flow, we are able to demonstrate that chain sets can be lifted to a chain transitive set if the given graph is complete.