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This article is cited in 1 scientific paper (total in 1 paper)
Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case
Rodrigo Gutierrez, Claudio Vidal Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile
Abstract:
This paper concerns with the study of the stability of one
equilibrium solution of an autonomous analytic Hamiltonian system in a
neighborhood of the equilibrium point with $1$-degree of freedom in the degenerate
case $H= q^4+ H_5+ H_6+\ldots$. Our main results complement the study initiated by Markeev in [9].
Keywords:
Hamiltonian system, equilibrium solution, type of stability, normal form, critical cases, Lyapunov’s Theorem, Chetaev’s Theorem
DOI:
https://doi.org/10.1134/S1560354717070097
References:
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Bibliographic databases:
MSC: 37C75, 34D20, 34A25 Received: 17.08.2017 Accepted:04.12.2017
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Citation:
Rodrigo Gutierrez, Claudio Vidal, “Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case”, Regul. Chaotic Dyn., 22:7 (2017), 880–892
Citation in format AMSBIB
\Bibitem{GutVid17}
\by Rodrigo Gutierrez, Claudio Vidal
\paper Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 7
\pages 880--892
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http://mi.mathnet.ru/eng/rcd297 http://mi.mathnet.ru/eng/rcd/v22/i7/p880
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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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