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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Simpson, D.J.W. (2017). Open Problems on Border-Collision Bifurcations. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_29
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DOI: https://doi.org/10.1007/978-3-319-55642-0_29
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