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Dokl. Akad. Nauk, 2018, Volume 479, Number 5, Pages 485–488
(Mi dan47527)
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This article is cited in 1 scientific paper (total in 1 paper)
On the stability of a periodic Hamiltonian system with one degree of freedom in a transcendental case
B. S. Bardinab a Moscow Aviation Institute (National Research University)
b Russian Academy of Sciences
Abstract:
AbstractThe stability of an equilibrium of a nonautonomous Hamiltonian system with one degree of freedom whose Hamiltonian function depends 2Ï-periodically on time and is analytic near the equilibrium is considered. The multipliers of the system linearized around the equilibrium are assumed to be multiple and equal to 1 orâ1. Sufficient conditions are found under which a transcendental case occurs, i.e., stability cannot be determined by analyzing the finite-power terms in the series expansion of the Hamiltonian about the equilibrium. The equilibrium is proved to be unstable in the transcendental case.
DOI:
https://doi.org/10.7868/S0869565218110014
English version:
Doklady Mathematics, 2018, 97:2, 161–163
Bibliographic databases:
UDC:
531.36
Linking options:
http://mi.mathnet.ru/eng/dan47527
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This publication is cited in the following articles:
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Boris S. Bardin, Víctor Lanchares, “Stability of a One-degree-of-freedom Canonical System in the Case of Zero Quadratic and Cubic Part of a Hamiltonian”, Regul. Chaotic Dyn., 25:3 (2020), 237–249
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