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Regular and Chaotic Dynamics, 2012, Volume 17, Issue 3-4, Pages 307–317
DOI: https://doi.org/10.1134/S1560354712030070 (Mi rcd404) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Determination of Nonlinear Stability for Low Order Resonances by a Geometric Criterion

Víctor Lancharesa, Ana I. Pascuala, Antonio Elipeb

a Departamento Matemáticas y Computación, CIME, Universidad de La Rioja, Univ. de La Rioja, 26004 Logroño, Spain
b Grupo de Mecánica Espacial-IUMA and Centro Universitario de la Defensa de Zaragoza, Univ. de Zaragoza, 50009 Zaragoza, Spain
Citations (1)
DOI: https://doi.org/10.1134/S1560354712030070
Abstract: We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under low order resonances. For resonances of order bigger than two there are several results giving stability conditions, in particular one based on the geometry of the phase flow and a set of invariants. In this paper we show that this geometric criterion is still valid for low order resonances, that is, resonances of order two and resonances of order one. This approach provides necessary stability conditions for both the semisimple and non-semisimple cases, with an appropriate choice of invariants.
Keywords: nonlinear stability, resonances, normal forms.
Funding agency Grant number
Ministry of Science and Innovation of Spanish MTM2011-28227-C02-02
AYA2008-05572
We acknowledge financial support from the Spanish Ministry of Science and Innovation (Projects MTM2011-28227-C02-02 and AYA2008-05572).
Received: 02.03.2012
Accepted: 22.06.2012
Bibliographic databases:
Document Type: Article
MSC: 34D20, 37J40, 70H05
Language: English
Citation: Víctor Lanchares, Ana I. Pascual, Antonio Elipe, “Determination of Nonlinear Stability for Low Order Resonances by a Geometric Criterion”, Regul. Chaotic Dyn., 17:3-4 (2012), 307–317
Citation in format AMSBIB
\Bibitem{LanPasEli12}
\by V{\'\i}ctor Lanchares, Ana I. Pascual, Antonio Elipe
\paper Determination of Nonlinear Stability for Low Order Resonances by a Geometric Criterion
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 3-4
\pages 307--317
\mathnet{http://mi.mathnet.ru/rcd404}
\crossref{https://doi.org/10.1134/S1560354712030070}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2956225}
\zmath{https://zbmath.org/?q=an:1256.34044}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2012RCD....17..307L}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865557157}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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