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Mathematics of the USSR-Sbornik, 1970, Volume 12, Issue 2, Pages 271–312
DOI: https://doi.org/10.1070/SM1970v012n02ABEH000922 (Mi sm3513) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Instability in a Hamiltonian system and the distribution of asteroids

A. D. Bruno
English version PDF (2373 kB) Citations (23)
References:
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DOI: https://doi.org/10.1070/SM1970v012n02ABEH000922
Abstract: The formal stability of periodic solutions is investigated for a Hamiltonian system in two degrees of freedom. The nature of the zones of instability is exhibited in the case of a resonance of order $q\geqslant3$. In contrast to classical theory, an isoenergetic reduction is not carried out. This permits unstable solutions close to periodic solutions to be studied in full. The results are applied to the restricted problem of three bodies, which allows us to explain qualitatively the nature of all gaps with $q\geqslant3$ in the distribution of asteroids.
Figures: 19.
Bibliography: 37 titles.
Received: 05.02.1970
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1970, Volume 83(125), Number 2(10), Pages 273–312
Bibliographic databases:
UDC: 517.913+521.41
MSC: 70H12, 70H14, 37J25, 37J45, 37J15, 70H33
Language: English
Original paper language: Russian
Citation: A. D. Bruno, “Instability in a Hamiltonian system and the distribution of asteroids”, Mat. Sb. (N.S.), 83(125):2(10) (1970), 273–312; Math. USSR-Sb., 12:2 (1970), 271–312
Citation in format AMSBIB
\Bibitem{Bru70}
\by A.~D.~Bruno
\paper Instability in a~Hamiltonian system and the distribution of asteroids
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 2(10)
\pages 273--312
\mathnet{http://mi.mathnet.ru/sm3513}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=274867}
\zmath{https://zbmath.org/?q=an:0217.12401}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 2
\pages 271--312
\crossref{https://doi.org/10.1070/SM1970v012n02ABEH000922}
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:432
    Russian version PDF:151
    English version PDF:10
    References:39
     
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