Abstract:
A time-periodic system with one degree of freedom is investigated. The system is assumed to have
an equilibrium position, in the vicinity of which the Hamiltonian is represented as a convergent
series.This series does not contain members of the second degree, whereas the members to some
finite degree ℓ do not depend explicitly on time. The algorithm for constructing a canonical
transformation is proposed that simplifies the structure of the Hamiltonian in members to
degree ℓ, inclusive. As an application, a special case is considered when the expansion of the
Hamiltonian begins with members of the third degree. For this case, sufficient conditions for
instability of the equilibrium are obtained depending on the forms of the fourth and fifth degrees.
Citation:
A. P. Markeev, “On the Birkhoff transformation in the case of complete degeneracy of the quadratic part of the Hamiltonian”, Nelin. Dinam., 11:2 (2015), 343–352; Regul. Chaotic Dyn., 20:3 (2015), 309–316
\Bibitem{Mar15}
\by A.~P.~Markeev
\paper On the Birkhoff transformation in the case of complete degeneracy of the quadratic part of the Hamiltonian
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 2
\pages 343--352
\mathnet{http://mi.mathnet.ru/nd484}
\transl
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 309--316
\crossref{https://doi.org/10.1134/S1560354715030077}
Citation in format AMSBIB
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