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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received: 17.08.2017 Accepted: 04.12.2017
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
Linking options:
https://www.mathnet.ru/eng/rcd297 https://www.mathnet.ru/eng/rcd/v22/i7/p880
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Abstract page: | 361 | References: | 38 |
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