On degenerate resonances and “vortex pairs” |
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Authors: | A D Morozov |
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Institution: | (1) Department of Mathematics and Mechanics, Nizhni Novgorod State University, Nizhni Novgorod, 603950, Russia |
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Abstract: | Hamiltonian systems with 3/2 degrees of freedom close to non-linear autonomous are studied. For unperturbed equations with
a nonlinearity in the form of a polynomial of the fourth or fifth degree, their coefficients are specified for which the period
on closed phase curves is not a monotone function of the energy and has extreme values of the maximal order. When the perturbation
is periodic in time, this non-monotonicity leads to the existence of degenerate resonances. The numerical study of the Poincaré
map was carried out and bifurcations related to the formation of the vortex pairs within the resonance zones were found. For
systems of a general form at arbitrarily small perturbations the absence of vortex pairs is proved. An explanation of the
appearance of these structures for the Poincaré map is presented.
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Keywords: | Resonances degenerate resonances Hamiltonian systems averaged systems separatrix vortex pairs Poincaré map |
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