Dissipative effects in piecewise linear dynamics

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May 2003, 3(2): 163-177. doi: 10.3934/dcdsb.2003.3.163

Dissipative effects in piecewise linear dynamics

1.	University of Exeter, School of Mathematics, North Park Road, Laver Building, Exeter EX4 4QE, United Kingdom

Received January 2002 Revised January 2003 Published February 2003

Abstract
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This work revisits a couple of well-known piecewise linear oscillators pointing out several unnoticed properties. In particular, for one of these oscillators we study under what conditions bounded motions are possible and investigate the effect of viscous damping on its trajectories. The article complements a relatively recent paper by Capecchi [10] and presents a non-trivial counterexample to the wide-spread belief according to which chaos is ubiquitous in piecewise linear systems.

Keywords: Non-smooth dynamics, monotone operators., plasticity.

Mathematics Subject Classification: 34A36, 47J40, 70K4.

Citation: Ciprian D. Coman. Dissipative effects in piecewise linear dynamics. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 163-177. doi: 10.3934/dcdsb.2003.3.163

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