Symplectic Calculation of Lyapunov Exponents

Salman Habib; Robert D. Ryne

doi:10.1103/PhysRevLett.74.70

Symplectic Calculation of Lyapunov Exponents

Salman Habib and Robert D. Ryne

Phys. Rev. Lett. 74, 70 – Published 2 January 1995

Abstract

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.

Received 24 June 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.70

Authors & Affiliations

Salman Habib^1,* and Robert D. Ryne^2,†

¹T-6, Theoretical Astrophysics and T-8, Elementary Particles and Field Theory Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
²AOT-1, Accelerator Physics and Special Projects Accelerator Operations and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

^*Electronic address: habib@eagle.lanl.gov
^†Electronic address: ryne@lanl.gov