DETERMINATION OF THE FREQUENCY VECTOR IN THE FOUR-DIMENSIONAL STANDARD MAPPING

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Abstract
Different numerical methods, for the computation of frequency versus initial conditions in the four-dimensional standard mapping, are proposed. The first method relies on the analytic properties of invariant rotational tori. A purely numerical technique was derived from an extension of a method suggested by M. Hénon for the two-dimensional mapping. A refinement of the last technique can be obtained implementing the frequency analysis introduced by J. Laskar. These methods agree up to some values of the coupling and perturbing parameters, close to the breakdown threshold for the onset of chaos. The transition to the chaotic regime is further confirmed by the computation of Lyapunov exponents and by suitable slice projections of the original mapping.

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