ON THE SUCCESSIVE ELIMINATION OF PERTURBATION HARMONICS

A practical method for the detailed exploration of two degrees of freedom dynamical systems is presented in this paper. This method is made up of several steps, in each of which we eliminate, via the introduction of suitable action-angle variables, the most relevant harmonic present in the Fourier expansion of the perturbation. In this way, at the end, one obtains a satisfactory description of the fine structure of secondary resonances, as well as detailed information about the size of chaotic layers and about the localization of regions filled up with invariant tori.