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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 1(5), Pages 140–156 (Mi msb3188)  

This article is cited in 1 scientific paper (total in 1 paper)

Some transversality theorems

S. M. Vishik


Abstract: In this paper transversality theorems are proved for canonical transformations, contact transformations, and transformations which preserve volume elements, as well as sections of a fiber bundle whose base and fiber are smooth manifolds. Let $\Omega$ be one of the mapping spaces mentioned, and let $L$ be a smooth submanifold in the space of $r$-jets of the germs of the mappings in $\Omega$. The transversality theorem asserts that a set of mappings in $\Omega$ whose $r$-jet extensions are transversal to $L$ is everywhere dense in $\Omega$.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1971, 14:1, 140–156

Bibliographic databases:

UDC: 513.83
MSC: Primary 57D35; Secondary 28A65
Received: 04.08.1970

Citation: S. M. Vishik, “Some transversality theorems”, Mat. Sb. (N.S.), 85(127):1(5) (1971), 140–156; Math. USSR-Sb., 14:1 (1971), 140–156

Citation in format AMSBIB
\Bibitem{Vis71}
\by S.~M.~Vishik
\paper Some transversality theorems
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 1(5)
\pages 140--156
\mathnet{http://mi.mathnet.ru/msb3188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=287562}
\zmath{https://zbmath.org/?q=an:0216.20701}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 1
\pages 140--156
\crossref{https://doi.org/10.1070/SM1971v014n01ABEH002609}


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  • http://mi.mathnet.ru/eng/msb/v127/i1/p140

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Arnol'd, “Lectures on bifurcations in versal families”, Russian Math. Surveys, 27:5 (1972), 54–123  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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