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The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system


Waldner, Franz; Hoover, William G; Hoover, Carol G (2014). The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system. Chaos, Solitons & Fractals, 60:68-76.

Abstract

We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed.

We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:2014
Deposited On:07 Apr 2014 11:18
Last Modified:05 Apr 2016 17:48
Publisher:Elsevier
ISSN:0960-0779
Publisher DOI:https://doi.org/10.1016/j.chaos.2014.01.006

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