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KIAM Preprint  59, Moscow, 2022
Authors: Batkhin A.B., Khaydarov Z.K.
Strong resonances in nonlinear Hamiltonian system
Abstract:
To investigate formal stability of an equilibrium of a multi-parameter Hamiltonian system with three degrees of freedom in the case of common position conditions for the existence of resonances of the third and fourth orders of multiplicity are found. These conditions are formulated as zeroes of polynomials from the coefficients of the characteristic polynomial of the linear part Hamilton system. We describe the partition of the set of stability in the space of coefficients of the characteristic polynomial into such parts where strong resonances are absent and where Brunos Theorem can be applied to determine the formal stability. We also consider some values of the coefficients of the characteristic polynomial at which the multiplicity of resonances is equal to two. Some example of a resonant set description is considered for a system with two parameters.
Keywords:
Hamiltonian system, normal form, resonant condition, Grobner basis, elimination ideal
Publication language: russian,  pages: 28
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Batkhin Alexander Borisovich,  orcid.org/0000-0001-8871-4697KIAM RAS
  • Khaydarov Zafar Khaydar ugli,  orcid.org/0000-0002-2580-4887Samarkand State University