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.
The equation of motion is
where is the temporal frequency of the electrostatic wave. Thus we can derive the Hamiltonian, choosing :
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 A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, 2nd ed., New York: Springer 1992 p. 238.
 J. Candy and W. Rozmus, "A Symplectic Integration Algorithm for Separable Hamiltonian Functions," Journal of Computational Physics 92, 1991 pp. 230–256. doi:10.1016/0021-9991(91)90299-Z.
 G. Zaslavsky, "Zaslavsky Web Map," Scholarpedia, 2(10): 3369, 2007. doi:10.4249/scholarpedia.3369.