Dissipative effects in piecewise linear dynamics

Ciprian D. Coman

doi:10.3934/dcdsb.2003.3.163

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2003, Volume 3, Issue 2: 163-177. Doi: 10.3934/dcdsb.2003.3.163

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Dissipative effects in piecewise linear dynamics

Ciprian D. Coman^1,

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

Received: January 2002

Revised: January 2003

Published: May 2003

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Abstract

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.

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Mathematics Subject Classification: 34A36, 47J40, 70K40.

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