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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 1, Pages 131–138
DOI: https://doi.org/10.1070/RD2006v011n01ABEH000339
(Mi rcd662)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the continuation of degenerate periodic orbits in Hamiltonian systems

E. Meletlidou, G. Stagika

University of Thessaloniki, Thessaloniki 54124, Greece
Citations (3)
Abstract: The continuation of non-isolated periodic orbits lying on the resonant invariant tori of an integrable Hamiltonian system with respect to a small perturbative parameter cannot be proved by a direct application of the continuation theorem, since their monodromy matrix possesses more than a single pair of unit eigenvalues. In this case one may use Poincaré's theorem which proves that, if the integrable part of the Hamiltonian is non-degenerate and the average value of the perturbing function, evaluated along the unperturbed periodic orbits, possesses a simple extremum on such an orbit, then this orbit can be analytically continued with respect to the perturbation. In the present paper we prove a criterion for the continuation of the non-isolated periodic orbits, for which this average value is constant along the periodic orbits of the resonant torus and Poincaré's theorem is not applicable. We apply the results in two such systems of two degrees of freedom.
Keywords: near-integrable Hamiltonian systems, periodic orbits, resonance.
Received: 06.05.2005
Accepted: 10.08.2005
Bibliographic databases:
Document Type: Article
MSC: 70F15, 70H08
Language: English
Citation: E. Meletlidou, G. Stagika, “On the continuation of degenerate periodic orbits in Hamiltonian systems”, Regul. Chaotic Dyn., 11:1 (2006), 131–138
Citation in format AMSBIB
\Bibitem{MelSta06}
\by E.~Meletlidou, G.~Stagika
\paper On the continuation of degenerate periodic orbits in Hamiltonian systems
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 1
\pages 131--138
\mathnet{http://mi.mathnet.ru/rcd662}
\crossref{https://doi.org/10.1070/RD2006v011n01ABEH000339}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2222437}
\zmath{https://zbmath.org/?q=an:1135.37323}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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