Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki"
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Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", 1983, Volume 22, Pages 3–55 (Mi intd61)  
This article is cited in 13 scientific papers (total in 14 papers)

Singularities in the calculus of variations

V. I. Arnol'd
Full-text PDF (3329 kB) Citations (14)
Abstract: A survey is given of theories of singularities of systems of rays and wave fronts, that is, singularities of systems of extremals of variational problems and solutions of the Hamilton–Jacobi equations near caustics. The problem of passing about an obstacle bounded by a smooth surface of general position is studied in detail. Theorems are proved on the normal forms of Lagrangian manifolds with singularities formed by rays of the system of extremals of a variational problem in the symplectic space of all oriented lines which tear off from the surface of the obstacle as well as theorems on Legendre manifolds with singularities formed by contact elements of a wave front and 1-jets of a solution of the Hamilton–Jacobi equation.
English version:
Journal of Soviet Mathematics, 1984, Volume 27, Issue 3, Pages 2679–2713
DOI: https://doi.org/10.1007/BF01084817
Bibliographic databases:
Document Type: Article
UDC: 515.164.14+517.374
Language: Russian
Citation: V. I. Arnol'd, “Singularities in the calculus of variations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 22, VINITI, Moscow, 1983, 3–55; J. Soviet Math., 27:3 (1984), 2679–2713
Citation in format AMSBIB
\Bibitem{Arn83}
\by V.~I.~Arnol'd
\paper Singularities in the calculus of variations
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1983
\vol 22
\pages 3--55
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd61}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=735439}
\zmath{https://zbmath.org/?q=an:0554.58010|0537.58012}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 27
\issue 3
\pages 2679--2713
\crossref{https://doi.org/10.1007/BF01084817}
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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