Linear Oscillator Perturbed by Plane Electrostatic Waves

A charged particle gyrating in a uniform magnetic field directed along the axis interacts with electrostatic waves, with equal wavenumbers and amplitudes but differing frequencies , propagating along the axis. Resonance occurs when (where is the cyclotron frequency). A stochastic web is then generated, as can be observed from its Poincaré map.

[2] A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, 2nd ed., New York: Springer 1992 p. 238.

[3] J. Candy and W. Rozmus, "A Symplectic Integration Algorithm for Separable Hamiltonian Functions," Journal of Computational Physics92, 1991 pp. 230–256. doi:10.1016/0021-9991(91)90299-Z.