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Mathematics of the USSR-Sbornik, 1973, Volume 19, Issue 1, Pages 139–156
DOI: https://doi.org/10.1070/SM1973v019n01ABEH001741 (Mi sm3001) 		 
This article is cited in 174 scientific papers (total in 174 papers)

On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II

N. K. Gavrilov, L. P. Shilnikov
English version PDF (1100 kB) Citations (174) Russian version article
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DOI: https://doi.org/10.1070/SM1973v019n01ABEH001741
Abstract: Dynamical systems are considered which are close to systems with a structurally unstable homoclinic curve. A definition of accessibility of a bifuration surface is given, and it is established that a bifurcation surface $H^1$ corresponding to systems with a structurally unstable homoclinic curve will be inaccessible from at least one side. Cases are singled out in which $H^1$ can be the boundary separating Morse–Smale systems from systems with a countable number of periodic motions.
Bibliography: 14 titles.
Received: 28.07.1972
Bibliographic databases:
UDC: 517.9
MSC: 58F10
Language: English
Original paper language: Russian
Citation: N. K. Gavrilov, L. P. Shilnikov, “On three-dimensional dynamical systems close to systems with a structurally unstable homoclinic curve. II”, Math. USSR-Sb., 19:1 (1973), 139–156
Citation in format AMSBIB
\Bibitem{GavShi73}
\by N.~K.~Gavrilov, L.~P.~Shilnikov
\paper On three-dimensional dynamical systems close to systems with a~struc\-tu\-rally unstable homoclinic curve.~II
\jour Math. USSR-Sb.
\yr 1973
\vol 19
\issue 1
\pages 139--156
\mathnet{http://mi.mathnet.ru//eng/sm3001}
\crossref{https://doi.org/10.1070/SM1973v019n01ABEH001741}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=334280}
\zmath{https://zbmath.org/?q=an:0258.58009}
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  • https://www.mathnet.ru/eng/sm/v132/i1/p139
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    This publication is cited in the following 174 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:885
    Russian version PDF:257
    English version PDF:20
    References:84
    First page:1
     
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