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 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2017, Volume 22, Issue 7, Pages 880–892 (Mi rcd297)

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

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Bibliographic databases:

MSC: 37C75, 34D20, 34A25
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 \mathnet{http://mi.mathnet.ru/rcd297} \crossref{https://doi.org/10.1134/S1560354717070097} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425980500009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042483855}