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This article is cited in 14 scientific papers (total in 14 papers)
Effective computations in modern dynamics
On the break-down threshold of invariant tori in four dimensional maps
A. Cellettia, C. Falcolinib, U. Locatellia a Dipartimento di Matematica,
Università di Roma Tor Vergata,
Via della Ricerca Scientifica 1, I-00133 Roma (Italy)
b Dipartimento di Matematica,
Università di Roma Tre,
Largo S. L. Murialdo 1, I-00146 Roma (Italy)
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 Padé 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.
Received: 27.09.2004
Citation:
A. Celletti, C. Falcolini, U. Locatelli, “On the break-down threshold of invariant tori in four dimensional maps”, Regul. Chaotic Dyn., 9:3 (2004), 227–253
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https://www.mathnet.ru/eng/rcd744 https://www.mathnet.ru/eng/rcd/v9/i3/p227
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