Multiple Island Chains in Primary Resonances.

We analyse the dynamics of a relativistic particle moving in a uniform magnetic field and perturbed by a stationary electrostatic wave. We show that a pulsed wave produces an infinite number of perturbing terms with the same winding number. The perturbation coupling alters the number of island chains as a function of the parameters of the wave. We also observe that the number of chains in is always even if the number of islands in each chain is odd.