Chaos, Ergodicity, and the Thermodynamics of Lower-Dimensional Time-Independent Hamiltonian Systems

Journal Article · Wed Aug 01 00:00:00 EDT 2001 · Phys.Rev.E

DOI:https://doi.org/10.1103/PhysRevE.65.016214· OSTI ID:1898838

Kandrup, Henry E. ^[1]; Sideris, I. V. ^[1]; Sideris, Ioannis V. ^[2]; Bohn, Courtlandt L. ^[3]

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1. Florida U., Inst. Fund. Theor.
2. Florida U.
3. Fermilab

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.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• DOE Contract Number: AC02-07CH11359
• OSTI ID: 1898838
• Report Number(s): FERMILAB-PUB-01-231-T; arXiv:astro-ph/0108038; oai:inspirehep.net:561624
• Journal Information: Phys.Rev.E, Journal Name: Phys.Rev.E Vol. 65
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS