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.
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
\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
\mathnet{http://mi.mathnet.ru/rcd297}
\crossref{https://doi.org/10.1134/S1560354717070097}
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Linking options:
https://www.mathnet.ru/eng/rcd297
https://www.mathnet.ru/eng/rcd/v22/i7/p880
This publication is cited in the following 2 articles:
Dmytro Chumachenko, Sergiy Yakovlev, Ievgen Meniailov, Kseniia Bazilevych, Halyna Padalko, Advances in Intelligent Systems and Computing, 1335, Congress on Intelligent Systems, 2021, 49
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
Citation in format AMSBIB
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