NUMERICAL INVESTIGATIONS OF THE STRUCTURE AROUND AN INVARIANT KAM TORUS USING THE FREQUENCY MAP ANALYSIS

The hierarchical structure around KAM tori is studied numerically on t he standard map, as a model problem, applying the Laskar frequency map analysis. The theoretical prediction recently given by Morbidelli and Giorgilli (J. Stat. Phys. 78 (1994)) about the existence of a neighbo rhood almost completely full of slave tori around a chief torus are re covered and extended to the near critical regime.