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

Henry E. Kandrup, Ioannis V. Sideris, and Courtlandt L. Bohn
Phys. Rev. E 65, 016214 – Published 20 December 2001
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Abstract

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 may be modeled by a stochastic-oscillator equation [cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)], linearized perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.

  • Received 16 August 2001

DOI:https://doi.org/10.1103/PhysRevE.65.016214

©2001 American Physical Society

Authors & Affiliations

Henry E. Kandrup*

  • Department of Astronomy, Department of Physics, and Institute for Fundamental Theory, University of Florida, Gainesville, Florida 32611

Ioannis V. Sideris

  • Department of Astronomy, University of Florida, Gainesville, Florida 32611

Courtlandt L. Bohn

  • Fermilab, Batavia, Illinois 60510

  • *Electronic address: kandrup@astro.ufl.edu
  • Electronic address: sideris@astro.ufl.edu
  • Electronic address: clbohn@fnal.gov

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Vol. 65, Iss. 1 — January 2002

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