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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
Normal Form Construction for Nearly-integrable Systems with Dissipation
Alessandra Cellettia, Christoph Lhotkab a Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma (Italy)
b Namur Center for Complex Systems, Départment de Mathématique, Université FUNDP, Rempart de la Vierge 8, B-5000 Namur (Belgium)
Аннотация:
We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a dissipative contribution is added. The vector field depends upon two parameters, namely the perturbing and dissipative parameters, and by a drift term. We study an $l$-dimensional, time-dependent vector field, which is motivated by mathematical models in Celestial Mechanics. Assuming to start with non-resonant initial conditions, we provide the construction of the normal form up to an arbitrary order. To construct the normal form, a suitable choice of the drift parameter must be performed. The normal form allows also to provide an explicit expression of the frequency associated to the normalized coordinates. We also give an example in which we construct explicitly the normal form, we make a comparison with a numerical integration, and we determine the parameter values and the time interval of validity of the normal form.
Ключевые слова:
dissipative system, normal form, non-resonant motion.
Поступила в редакцию: 27.01.2012 Принята в печать: 08.05.2012
Образец цитирования:
Alessandra Celletti, Christoph Lhotka, “Normal Form Construction for Nearly-integrable Systems with Dissipation”, Regul. Chaotic Dyn., 17:3-4 (2012), 273–292
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd402 https://www.mathnet.ru/rus/rcd/v17/i3/p273
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