Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case

2017, Volume 22, Number 7, pp. 880-892

Author(s): Gutierres R., Vidal C.

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 $H= q^4+ H_5+ H_6+\cdots$. Our main results complete 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

Citation: Gutierres R., Vidal C., Stability of Equilibrium Points for a Hamiltonian Systems with One Degree of Freedom in One Degenerate Case, Regular and Chaotic Dynamics, 2017, Volume 22, Number 7, pp. 880-892

DOI: 10.1134/S1560354717070097

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