Abstract
Perhaps we should wrap up this volume by asking why nonsmooth dynamics is the subject of a three month Intensive Research Program at the CRM (February to April 2016), why it was the subject of more than 2000 papers published in 2015 (and only 700 in the year 2000; data from Thomson Reuters Web of Science), and why it is a growing presence at international conferences involving mathematics and its applications. We briefly survey here why discontinuity is not only important in modeling real-world systems, but is also a fundamental property of many nonlinear systems.
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Notes
- 1.
For other examples try a Hill, tanh, or error function with complex argument \({\sigma }+{i}\rho \).
References
C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I. Asymptotic Methods and Perturbation Theory (Springer, New York, 1999)
A.F. Filippov, Differential Equations with Discontinuous Righthand Sides (Kluwer Academic Publishers, Dordrecht, 1988) (Russian 1985)
M.R. Jeffrey, The ghosts of departed quantities in switches and transitions, preprint (2015)
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Jeffrey, M.R. (2017). Why Nonsmooth?. 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_18
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DOI: https://doi.org/10.1007/978-3-319-55642-0_18
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