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Tangencies: The Shape of the Discontinuity Surface

In: Hidden Dynamics

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  • Mike R. Jeffrey

    (University of Bristol, Department of Engineering Mathematics)

Abstract

The presence of a discontinuity introduces a new elementary singularity to local dynamical systems theory, in the form of a tangency tangency between the flow flow and the discontinuity surface discontinuity surface . This chapter sets out the basic geometry of flows around such tangencies. They underlie the most important qualitative features of piecewise-smooth dynamics, forming the boundaries of sliding sliding regions, and points where the flow is poised between smooth evolution and switching.

Suggested Citation

  • Mike R. Jeffrey, 2018. "Tangencies: The Shape of the Discontinuity Surface," Springer Books, in: Hidden Dynamics, chapter 0, pages 103-124, Springer.
  • Handle: RePEc:spr:sprchp:978-3-030-02107-8_6
    DOI: 10.1007/978-3-030-02107-8_6
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