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

Multiflows: A New Technique for Filippov Systems and Differential Inclusions