Strong resonances in nonlinear Hamiltonian system
Сильные резонансы в нелинейной системе Гамильтона

Alexander Borisovich Batkhin, Zafar Khaydar ugli Khaydarov
2022 Keldysh Institute Preprints  
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
more » ... 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.
doi:10.20948/prepr-2022-59 fatcat:khsrgbhrpnenjb33kwdjcquiue