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 that of the invariant attractors, as well as to constrain the drift of a periodic orbit within Arnold's tongues in the parameter space.
Celletti, A., & Di Ruzza, S. (2011). Periodic and quasi-periodic attractors of the dissipative standard map. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., 16(1), 151-171 [10.3934/dcdsb.2011.16.151].
Tipologia: | Articolo su rivista | |
Citazione: | Celletti, A., & Di Ruzza, S. (2011). Periodic and quasi-periodic attractors of the dissipative standard map. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B., 16(1), 151-171 [10.3934/dcdsb.2011.16.151]. | |
IF: | Con Impact Factor ISI | |
Lingua: | English | |
Settore Scientifico Disciplinare: | Settore MAT/07 - Fisica Matematica | |
Revisione (peer review): | Esperti anonimi | |
Tipo: | Articolo | |
Rilevanza: | Rilevanza internazionale | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.3934/dcdsb.2011.16.151 | |
Stato di pubblicazione: | Pubblicato | |
Data di pubblicazione: | 2011 | |
Titolo: | Periodic and quasi-periodic attractors of the dissipative standard map | |
Autori: | ||
Autori: | Celletti, A; Di Ruzza, S | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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