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Dokl. Akad. Nauk, 2018, Volume 479, Number 5, Pages 485–488 (Mi dan47527)  

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 2π-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 or–1. 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

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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet
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