Abstract
The collision of a fixed point with a switching manifold in a piecewise-smooth continuous map, known as a border-collision bifurcation, can give rise to a seemingly endless zoo of complicated dynamics. An understanding of these dynamics, which are described merely by piecewise-linear continuous maps, is one of the most fundamental problems in nonsmooth bifurcation theory. This extended abstract recalls some aspects of border-collision bifurcations and provides a list of pertinent open problems for future research.
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