Journal Article

On the relationship between instability and Lyapunov times for the three-body problem

D. J. Urminsky and D. C. Heggie

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 392, issue 3, pages 1051-1059
Published in print January 2009 | ISSN: 0035-8711
Published online January 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.14149.x
On the relationship between instability and Lyapunov times for the three-body problem

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In this study we consider the relationship between the survival time and the Lyapunov time for three-body systems. It is shown that the Sitnikov problem exhibits a two-part power-law relationship as demonstrated by Mikkola & Tanikawa for the general three-body problem. Using an approximate Poincaré map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the three-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general three-body problem.

Keywords: stellar dynamics; celestial mechanics; time

Journal Article.  5295 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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