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Preprint . 1994
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Physical Review Letters
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Symplectic Calculation of Lyapunov Exponents

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 02 Jan 1995Embargo end date: 01 Jan 1994 English Publisher:American Physical Society (APS)Journal:Physical Review Letters, volume 74, pages 70-73 (issn: 0031-9007, eissn: 1079-7114, Copyright policy )
Authors: Habib, Salman; Ryne, Robert D.;

doi: 10.1103/physrevlett.74.70 , 10.48550/arxiv.chao-dyn/9406010

pmid: 10057701

arXiv: chao-dyn/9406010

Symplectic Calculation of Lyapunov Exponents

Abstract

The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to develop a new method for the calculation of Lyapunov exponents of such systems. Our approach avoids the renormalization and reorthogonalization of usual techniques. It is also easily extendible to damped systems. We apply our method to two examples of physical interest: a model system that describes the beam halo in charged particle beams and the driven van der Pol oscillator.

10 pages, uuencoded PostScript (figures included), LA-UR-94-2169

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Keywords

FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, General Relativity and Quantum Cosmology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
43
Top 10%
Top 10%
Top 10%
Green