This article is cited 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.

MSC: 37C75, 34D20, 34A25

Received: 17.08.2017
Accepted: 04.12.2017

Language: English

DOI: 10.1134/S1560354717070097

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