Integral Curves of a Vector Field with a Fractal Discontinuity
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Nonsmooth systems are typically studied with smooth or piecewise-smooth boundaries between smooth vector fields, especially with linear or hyper-planar boundaries. What happens when there is a boundary that is not as simple, for example a fractal? Can a solution to such a system slide or “chatter” along this boundary? It turns out that the dynamics is rather fascinating, and yet contained within A.F. Filippov’s theory (as promised in Utkin, Comments for the continuation method by A.F. Filippov for discontinuous systems, parts I and II,  from this volume).