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This article is cited in 2 scientific papers (total in 2 papers)
On Resonances in Hamiltonian Systems with Three Degrees of Freedom
Alexander A. Karabanova, Albert D. Morozovb a Sir Peter Mansfield Imaging Centre, School of Physics and Astronomy, University of Nottingham, University Park, NG7 2RD, UK
b Lobachevsky State University of Nizhny Novgorod,
pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
Abstract:
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.
Keywords:
Hamiltonian systems, resonances, topological structures.
Received: 26.04.2019 Accepted: 05.11.2019
Citation:
Alexander A. Karabanov, Albert D. Morozov, “On Resonances in Hamiltonian Systems with Three Degrees of Freedom”, Regul. Chaotic Dyn., 24:6 (2019), 628–648
Linking options:
https://www.mathnet.ru/eng/rcd1030 https://www.mathnet.ru/eng/rcd/v24/i6/p628
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Abstract page: | 143 | References: | 32 |
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