Аннотация:
We address the dynamics of near-integrable Hamiltonian systems with 3 degrees of freedom in extended vicinities of unperturbed resonant invariant Liouville tori. The main attention is paid to the case where the unperturbed torus satisfies two independent resonance conditions. In this case the average dynamics is 4-dimensional, reduced to a generalised motion under a conservative force on the 2-torus and is generically non-integrable. Methods of differential topology are applied to full description of equilibrium states and phase foliations of the average system. The results are illustrated by a simple model combining the non-degeneracy and non-integrability of the isoenergetically reduced system.
This work has been partially supported by the Russian Foundation for Basic Research under
grants no. 18-01-00306 and by the Ministry of Education and Science of the Russian Federation
(project no. 1.3287.2017/PCh).
Поступила в редакцию: 26.04.2019 Принята в печать: 05.11.2019
Образец цитирования:
Alexander A. Karabanov, Albert D. Morozov, “On Resonances in Hamiltonian Systems with Three Degrees of Freedom”, Regul. Chaotic Dyn., 24:6 (2019), 628–648
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\by Alexander A. Karabanov, Albert D. Morozov
\paper On Resonances in Hamiltonian Systems with Three Degrees of Freedom
\jour Regul. Chaotic Dyn.
\yr 2019
\vol 24
\issue 6
\pages 628--648
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1030
https://www.mathnet.ru/rus/rcd/v24/i6/p628
Эта публикация цитируется в следующих 2 статьяx:
L. Biasco, L. Chierchia, “Global properties of generic real–analytic nearly–integrable Hamiltonian systems”, Journal of Differential Equations, 385 (2024), 325
T. Combot, A. J. Maciejewski, M. Przybylska, “Non-integrability of a model of elastic dumbbell satellite”, Nonlinear Dyn., 106:1 (2021), 125–146
Цитирование в формате AMSBIB
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