Tangencies: The Shape of the Discontinuity Surface
The presence of a discontinuity introduces a new elementary singularity to local dynamical systems theory, in the form of a tangency between the flow and the 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 regions, and points where the flow is poised between smooth evolution and switching.
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