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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 4, Pages 519–528
DOI: https://doi.org/10.1070/RD2004v009n04ABEH000294 (Mi rcd760) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Effective computations in modern dynamics

The stability of the Thomson heptagon

D. S. Schmidt

Department of Electrical & Computer Engineering and Computer Science, University of Cincinnati, 894 Rhodes Hall, Cincinnati, USA 45221-0030
Citations (4)
DOI: https://doi.org/10.1070/RD2004v009n04ABEH000294
Abstract: In 1882 J. J. Thomson had claimed in his Adams prize essay "The motion of vortex rings" that a ring of seven vortices would be unstable. It was shown later that linear analysis can not decide stability in this case. In 1999 Cabral and Schmidt proved stability by calculating the higher order terms in the normal form of the Hamiltonian with the help of POLYPACK, a personal algebraic processor. The work is repeated here with the help of the more readily available computer algebra system MATHEMATICA.
Received: 04.06.2004
Bibliographic databases:
Document Type: Article
MSC: 76B47, 34K18, 34K20
Language: English
Citation: D. S. Schmidt, “The stability of the Thomson heptagon”, Regul. Chaotic Dyn., 9:4 (2004), 519–528
Citation in format AMSBIB
\Bibitem{Sch04}
\by D.~S.~Schmidt
\paper The stability of the Thomson heptagon
\jour Regul. Chaotic Dyn.
\yr 2004
\vol 9
\issue 4
\pages 519--528
\mathnet{http://mi.mathnet.ru/rcd760}
\crossref{https://doi.org/10.1070/RD2004v009n04ABEH000294}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2109096}
\zmath{https://zbmath.org/?q=an:1102.76027}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..519S}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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