Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems

Details Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems Chaos, ergodicity, and the thermodynamics of lower-dimensional Hamiltonian systems

2001-08-02

arxiv.org/abs/astro-ph/0108038v1

Phys.Rev. E65 (2002) 016214

Astronomy and Astrophysics

Astrophysics

19 pp. including 14 Figures, uses Phys. Rev. macros

Scientific paper

10.1103/PhysRevE.65.016214

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability can be modeled by a stochastic-oscillator equation (cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)), linearised perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.

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