Search results for "Standard map"
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Periodic and quasi-periodic orbits of the dissipative standard map
2011
We present analytical and numerical investigations of the dynamics of the dissipative standard map. We first study the existence of periodic orbits by using a constructive version of the implicit function theorem; then, we introduce a parametric representation, which provides the interval of the drift parameter ensuring the existence of a periodic orbit with a given period. The determination of quasi--periodic attractors is efficiently obtained using the parametric representation combined with a Newton's procedure, aimed to reduce the error of the approximate solution provided by the parametric representation. These methods allow us to relate the drift parameter of the periodic orbits to th…
Nearly-integrable dissipative systems and celestial mechanics
2010
The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KA…