Multiflows: A New Technique for Filippov Systems and Differential Inclusions

Abstract: The flow is very useful in studying dynamical systems. However, many modern systems--notably differential inclusions--do not have unique solutions, and therefore cannot be described by flows. Richard McGehee has proposed an object, the multiflow, in order to use the topological techniques developed for flows in this setting. In this paper we will introduce multiflows and prove that under basic conditions, differential inclusions give rise to multiflows. This paper will also outline the most prominent example of differential inclusions, Filippov systems, as motivation. In addition, several results on differential inclusions, such as the existence theorem, are reproven here in order to create a self-contained work.