Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems

Details Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems

2002-11-12

arxiv.org/abs/astro-ph/0211248v2

Phys.Lett. A311 (2003) 165

Astronomy and Astrophysics

Astrophysics

6 pages, 3 PostScript figures

Scientific paper

10.1016/S0375-9601(03)00497-3

Recent work has shown that statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable, albeit less accurate, estimates of the largest Lyapunov exponent ${\chi}$ in lower-dimensional Hamiltonian systems. This letter explores the detailed assumptions incorporated into these arguments. The predicted values of ${\chi}$ are insensitive to most of these details, which can in any event be relaxed straightforwardly, but {\em can} depend sensitively on the nongeneric form of the auto-correlation function characterising the time-dependence of an orbit. This dependence on dynamics implies a fundamental limitation to the application of thermodynamic arguments to such lower-dimensional systems.

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