Symplectic Calculation of Lyapunov Exponents

Details Symplectic Calculation of Lyapunov Exponents Symplectic Calculation of Lyapunov Exponents

1994-06-26

arxiv.org/abs/chao-dyn/9406010v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, uuencoded PostScript (figures included), LA-UR-94-2169

Scientific paper

10.1103/PhysRevLett.74.70

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.

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