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Moscow Mathematical Journal, 2007, Volume 7, Number 1, Pages 1–20
DOI: https://doi.org/10.17323/1609-4514-2007-7-1-1-20
(Mi mmj268)
 

This article is cited in 5 scientific papers (total in 5 papers)

A counterexample to a multidimensional version of the weakened Hilbert's 16th problem

M. Bobieński, H. Żołądek

Institute of Mathematics, Warsaw University
Full-text PDF Citations (5)
References:
Abstract: In the weakened 16th Hilbert's Problem one asks for a bound on the number of limit cycles which appear after a polynomial perturbation of a planar polynomial Hamiltonian vector field. It is known that this number is finite for an individual vector field. In the multidimensional generalization of this problem one considers polynomial perturbation of a polynomial vector field with an invariant plane supporting a Hamiltonian dynamics. We present an explicit example of such perturbation with an infinite number of limit cycles which accumulate at some separatrix loop.
Key words and phrases: Polynomial vector field, limit cycle, invariant manifold, Abelian integral.
Received: January 19, 2006; in revised form June 7, 2006
Bibliographic databases:
MSC: 34C07, 34C08
Language: English
Citation: M. Bobieński, H. Żołądek, “A counterexample to a multidimensional version of the weakened Hilbert's 16th problem”, Mosc. Math. J., 7:1 (2007), 1–20
Citation in format AMSBIB
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\by M.~Bobie{\'n}ski, H.~{\.Z}o\l {\k a}dek
\paper A counterexample to a~multidimensional version of the weakened Hilbert's 16th problem
\jour Mosc. Math.~J.
\yr 2007
\vol 7
\issue 1
\pages 1--20
\mathnet{http://mi.mathnet.ru/mmj268}
\crossref{https://doi.org/10.17323/1609-4514-2007-7-1-1-20}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2324554}
\zmath{https://zbmath.org/?q=an:05202833}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261708300001}
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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