On the break-down threshold of invariant tori in four dimensional maps

We investigate the break–down of invariant tori in a four dimensional standard mapping for different values of the coupling parameter. We select various two–dimensional frequency vectors, having eventually one or both components close to a rational value. The dynamics of this model is very reach and depends on two parameters, the perturbing and coupling parameters. Several techniques are introduced to determine the analyticity domain (in the complex perturbing parameter plane) and to compute the break–down threshold of the invariant tori. In particular, the analyticity domain is recovered by means of a suitable implementation of Pad´e approximants. The break–down threshold is computed through a suitable extension of Greene’s method to four dimensional systems. Frequency analysis is implemented and compared with the previous techniques.