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.
Categories: astro-ph nlin.CD