Abstract:
A general method is presented for constructing a nonlinear canonical transformation,
which makes it possible to introduce local variables in a neighborhood of periodic motions
of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for
investigating the behavior of the Hamiltonian system in the vicinity of its periodic trajectories.
In particular, it can be applied to solve the problem of orbital stability of periodic motions.
Keywords:
normal form, KAM theory, orbital stability, periodic orbit, Hamiltonian system, canonical transformation.
This research was supported by the grant of the Russian Science Foundation (project 22-21-00729) and was carried out at the Moscow Aviation Institute (National Research University).
Citation:
Boris S. Bardin, “On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom”, Regul. Chaotic Dyn., 28:6 (2023), 878–887
\Bibitem{Bar23}
\by Boris S. Bardin
\paper On the Method of Introduction of Local Variables in a Neighborhood of Periodic Solution of a Hamiltonian System with Two Degrees of Freedom
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 6
\pages 878--887
\mathnet{http://mi.mathnet.ru/rcd1239}
\crossref{https://doi.org/10.1134/S1560354723060059}
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https://www.mathnet.ru/eng/rcd1239
https://www.mathnet.ru/eng/rcd/v28/i6/p878
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