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 Bruno’s 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.
Publisher
Keldysh Institute of Applied Mathematics
Reference18 articles.
1. Брюно А. Д. О типах устойчивости в системах Гамильтона // Препринты ИПМ им. М.В.Келдыша. Москва, 2020. № 21. С. 1—24. https://doi.org/10.20948/prepr-2020-21.
2. Зигель К., Мозер Ю. Лекции по небесной механике. Ижевск : НИЦ .Регулярная и хаотическая динамика., 2001. 384 с.
3. Маркеев А. П. Точки либрации в небесной механике и космодинамике. М. : Гл. ред. физ.-мат. литер. изд-ва .Наука., 1978. 352 с.
4. Moser J. New aspects in the theory of stability of Hamiltonian Systems // Comm. Pure Appl. Math. 1958. Vol. 11, no. 1. P. 81–114.
5. Батхин А. Б., Брюно А. Д., Варин В. П. Множества устойчивости многопараметрических гамильтоновых систем // Прикладная математика и механика. 2012. Т. 76, № 1. С. 80—133.
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