Abstract
The study of nonsmooth dynamical systems is reaching a turning point. As the theory of bifurcations and chaos in low dimensions appear now to be coming of age, attention is turning to higher dimensions. This brings new challenges for the concept of solutions of a nonsmooth system with multiple dimensions and complex discontinuity geometries. There are a range of solution concepts for nonsmooth systems, and here we highlight how each is valid in different contexts, we discuss the extent to which they are consistent, and that only together do they allow us to tackle higher dimensional nonsmooth systems with a view to applications.
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