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2013
Impact Factor

Alexandr Karabanov

167610, Cernova,3a, Syktyvkar
Department of Mathematics of Ural Division of RAS

Publications:

Karabanov A. A., Morozov A. D.
To the theory of coupled oscillations passing through the resonance
2006, vol. 11, no. 2, pp.  259-268
Abstract
The problem of coupled oscillations is considered in the case when a stable equilibrium of a globally averaged system passes through a resonance curve. Questions of persistence of invariant tori and transition to a self-synchronization are particularly discussed.
Keywords: near-integrable systems, coupled oscillations, resonances, self-synchronization
Citation: Karabanov A. A., Morozov A. D.,  To the theory of coupled oscillations passing through the resonance , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 259-268
DOI: 10.1070/RD2006v011n02ABEH000349
Karabanov A. A.
Resonances in Four-Dimensional Quasi-Hamiltonian Systems: Analysis and Simulations
2001, vol. 6, no. 1, pp.  17-32
Abstract
The problem of qualitative behaviour of four-dimensional quasi-Hamiltonian system in a neighbourhood of a fixed resonance is considered. The general analytical grounds of the problem are touched upon. We turn to the global analysis of special three-dimensional system averaged near the resonance. Furthermore, a checking the theory against numerical simulations is made. Two physical examples, revealing an irregular resonant dynamics, are studied.
Citation: Karabanov A. A.,  Resonances in Four-Dimensional Quasi-Hamiltonian Systems: Analysis and Simulations, Regular and Chaotic Dynamics, 2001, vol. 6, no. 1, pp. 17-32
DOI:10.1070/RD2001v006n01ABEH000162

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