Probability distributions of local Lyapunov exponents for Hamiltonian systems
- The James Franck Institute and Department of Chemistry, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637 (United States)
We calculate the probability distributions of the largest local Lyapunov exponent for three Hamiltonian systems at different values of the energy [ital E], for a set of increasing values of the length in which the trajectory is partitioned. The systems we study are the Henon-Heiles model and the classical Ar[sub 3] and Ar[sub 7] clusters. We show that these distributions contain much information about the dynamics of the system and, in particular, can be used to study the evolution of ergodic properties as the internal energy of the system increases; therefore, even though the inequivalence of chaos and ergodicity does not allow one to consider Lyaponov exponents to be a direct measure of ergodicity, the sample distributions of short-term Lyapunov exponents can be used to evaluate the extent of ergodic behavior in the various situations.
- DOE Contract Number:
- FG02-86ER13488
- OSTI ID:
- 6521162
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 47:5; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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664500* -- Special Atoms & Molecules-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ARGON
ATOMIC MODELS
CALCULATION METHODS
DISTRIBUTION
DISTRIBUTION FUNCTIONS
ELEMENTS
FLUIDS
FUNCTIONS
GASES
HAMILTONIANS
LYAPUNOV METHOD
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MOLECULAR MODELS
NONMETALS
PHASE SPACE
PROBABILITY
QUANTUM OPERATORS
RARE GASES
SPACE
TRAJECTORIES