- 04-322 Celletti A., Falcolini C., Locatelli U.
- Status: R
On the break-down threshold of invariant tori in
four dimensional maps
Oct 11, 04
(auto. generated ps),
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Abstract. 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 Pade' 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.