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Regular and Chaotic Dynamics, 2006, Volume 11, Issue 1, Pages 83–102
DOI: https://doi.org/10.1070/RD2006v011n01ABEH000336
(Mi rcd659)
 

This article is cited in 2 scientific papers (total in 2 papers)

A model for separatrix splitting near multiple resonances

M. Rudnev, V. Ten

Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
Citations (2)
Abstract: We propose and study a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity $1+m$, $m \geqslant 0$. Physically, the model represents a toroidal pendulum, coupled with a Liouville-integrable system of $n$ non-linear rotators via a small analytic potential. The global bifurcation problem is set-up for the $n+1$ dimensional isotropic manifold, corresponding to a specific homoclinic orbit of the toroidal pendulum. The splitting of this manifold can be described by a scalar function on the $n$-torus. A sharp estimate for its Fourier coefficients is proven. It generalizes to a multiple resonance normal form of a convex analytic Liouville near-integrable Hamiltonian system. The bound then is exponentially small.
Keywords: near-integrable Hamiltonian systems, resonances, splitting of separatrices.
Received: 30.05.2005
Accepted: 25.11.2005
Bibliographic databases:
Document Type: Article
MSC: 70H08, 70H20
Language: English
Citation: M. Rudnev, V. Ten, “A model for separatrix splitting near multiple resonances”, Regul. Chaotic Dyn., 11:1 (2006), 83–102
Citation in format AMSBIB
\Bibitem{RudTen06}
\by M. Rudnev, V. Ten
\paper A model for separatrix splitting near multiple resonances
\jour Regul. Chaotic Dyn.
\yr 2006
\vol 11
\issue 1
\pages 83--102
\mathnet{http://mi.mathnet.ru/rcd659}
\crossref{https://doi.org/10.1070/RD2006v011n01ABEH000336}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2222434}
\zmath{https://zbmath.org/?q=an:1133.70328}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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