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

Balsa Terzic·Henry E. Kandrup
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Abstract

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 $χ$ in lower-dimensional Hamiltonian systems. This letter explores the detailed assumptions incorporated into these arguments. The predicted values of $χ$ 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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BibTeXRIS

Balsa Terzic, Henry E. Kandrup. 2003-03-18. Semi-Analytic Estimates of Lyapunov Exponents in Lower-Dimensional Systems. https://doi.org/10.1016/s0375-9601(03)00497-3

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