Integral Curves of a Vector Field with a Fractal Discontinuity

Conference paper
Part of the Trends in Mathematics book series (TM, volume 8)

Abstract

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, [2] from this volume).

References

  1. 1.
    A.F. Filippov, Differential Equations with Discontinuous Righthand Sides (Kluwer Academic Publishers, Dordrecht, 1988)Google Scholar
  2. 2.
    V.I. Utkin, Comments for the continuation method by A.F. Filippov for discontinuous systems, parts I and II, this volumeGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of Engineering MathematicsUniversity of BristolBristolUK

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