Symplectic calculation of Lyapunov exponents

Journal Article · Sun Jan 01 23:00:00 EST 1995 · Physical Review Letters; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.74.70· OSTI ID:6869840

Habib, S; Ryne, R D ^[1]

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1. T-6, Theoretical Astrophysics and T-8, Elementary Particles and Field Theory Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States) AOT-1, Accelerator Physics and Special Projects Accelerator Operations and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to develop a new method for the calculation of Lyapunov exponents of such systems. Our approach avoids the renormalization and reorthogonalization of usual techniques. It is also easily extendible to damped systems. We apply our method to two examples of physical interest: a model system that describes the beam halo in charged particle beams and the driven van der Pol oscillator.

• OSTI ID: 6869840
• Journal Information: Physical Review Letters; (United States), Journal Name: Physical Review Letters; (United States) Vol. 74:1; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
661300 -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ATTRACTORS
CALCULATION METHODS
DAMPING
DATA
EIGENVALUES
ELECTRONIC EQUIPMENT
EQUIPMENT
HAMILTONIANS
INFORMATION
LYAPUNOV METHOD
MATHEMATICAL OPERATORS
MATRICES
NUMERICAL DATA
ORTHOGONAL TRANSFORMATIONS
OSCILLATORS
QUANTUM OPERATORS
RENORMALIZATION
STOCHASTIC PROCESSES
THEORETICAL DATA
TRAJECTORIES
TRANSFORMATIONS