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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 1, Pages 95–111
DOI: https://doi.org/10.1070/RD2005v010n01ABEH000303
(Mi rcd699)
 

This article is cited in 8 scientific papers (total in 8 papers)

Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances

C. Vidal, F. Dos Santos

Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, Recife-Pe, Brasil
Citations (8)
Abstract: The problem of the stability of an equilibrium position of a nonautonomous $2 \pi$-periodic Hamiltonian system with $n$ degrees of freedom ($n \geqslant 2$), in a nonlinear setting, is studied in the presence of a single third and fourth order resonance. We give conditions of instability in the sense of Lyapunov and formal stability of the equilibrium position, depending on the coefficients of the Hamiltonian function.
Keywords: periodic Hamiltonian system, Lyapunov stability, formal stability, resonance, normal form.
Received: 30.08.2004
Accepted: 07.12.2004
Bibliographic databases:
Document Type: Article
MSC: 37C75, 34D20, 34A25
Language: English
Citation: C. Vidal, F. Dos Santos, “Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances”, Regul. Chaotic Dyn., 10:1 (2005), 95–111
Citation in format AMSBIB
\Bibitem{VidDos05}
\by C.~Vidal, F.~Dos Santos
\paper Stability of equilibrium positions of periodic Hamiltonian systems under third and fourth order resonances
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 1
\pages 95--111
\mathnet{http://mi.mathnet.ru/rcd699}
\crossref{https://doi.org/10.1070/RD2005v010n01ABEH000303}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2136833}
\zmath{https://zbmath.org/?q=an:1076.37050}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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