Kirill Morozov
prosp. Gagarina 23, Nizhni Novgorod, 603950 Russia
Lobachevsky State University of Nizhni Novgorod
Publications:
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Morozov A. D., Morozov K. E.
Abstract
The paper presents a brief review of results on the theory of nonlinear resonance in systems
with $\frac{3}{2}$ degrees of freedom. We discuss the averaged systems near resonance levels, distinguish
nondegenerate and degenerate resonances, and describe typical phase portraits of the corresponding
first- and second-approximation systems. Conditions for the existence of resonant periodic
solutions are formulated, and the appearance of invariant two-dimensional tori is discussed. Special
attention is paid to resonance zones near degenerate energy levels. Two illustrative examples
are presented, including the occurrence of a degenerate resonance inside a nondegenerate resonance
zone and the appearance of vortex pairs in the Poincaré map. The authors dedicate the
article to V.S. Afraimovich, an outstanding specialist in dynamical systems, on the occasion of
his 80th birthday.
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