Abstract
The 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.
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Original Russian Text © B.S. Bardin, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 5, pp. 485–488.
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Bardin, B.S. On the Stability of a Periodic Hamiltonian System with One Degree of Freedom in a Transcendental Case. Dokl. Math. 97, 161–163 (2018). https://doi.org/10.1134/S1064562418020163
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DOI: https://doi.org/10.1134/S1064562418020163