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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.:
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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1988, Volume 33, Pages 55–112 (Mi intd107)  

This article is cited in 13 scientific papers (total in 13 papers)

Singular Lagrangian manifolds and their Lagrangian mappings

A. B. Givental'


Abstract: The paper examines the singularity theory of Lagrangian manifolds and its connection with variational calculus, classification of Coxeter groups, and symplectic topology. We consider the application of the theory to the problem of going past an obstacle, to partial differential equations, and to the analysis of singularities of ray systems.

Full text: PDF file (3397 kB)

English version:
Journal of Soviet Mathematics, 1990, 52:4, 3246–3278

Bibliographic databases:

UDC: 515.164.15+514.763.337

Citation: A. B. Givental', “Singular Lagrangian manifolds and their Lagrangian mappings”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 33, VINITI, Moscow, 1988, 55–112; J. Soviet Math., 52:4 (1990), 3246–3278

Citation in format AMSBIB
\Bibitem{Giv88}
\by A.~B.~Givental'
\paper Singular Lagrangian manifolds and their Lagrangian mappings
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1988
\vol 33
\pages 55--112
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd107}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=967765}
\zmath{https://zbmath.org/?q=an:0900.58013|0731.58023}
\transl
\jour J. Soviet Math.
\yr 1990
\vol 52
\issue 4
\pages 3246--3278
\crossref{https://doi.org/10.1007/BF01095250}


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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. M. Zakalyukin, R. M. Roberts, “On stable singular Lagrangian varieties”, Funct. Anal. Appl., 26:3 (1992), 174–178  mathnet  crossref  mathscinet  zmath  isi
    2. A. Kh. Rakhimov, “Singularities of Riemannian Invariants”, Funct. Anal. Appl., 27:1 (1993), 39–50  mathnet  crossref  mathscinet  zmath  isi
    3. O. M. Myasnichenko, “Geodesics of the Boundary in the Obstacle Problem and Unfurled Swallowtails”, Funct. Anal. Appl., 29:2 (1995), 138–139  mathnet  crossref  mathscinet  zmath  isi
    4. O. M. Myasnichenko, “Direct Product of Unfurled Swallowtails in the Problem of Going around an Obstacle”, Funct. Anal. Appl., 30:4 (1996), 230–236  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. V. M. Zakalyukin, O. M. Myasnichenko, “Lagrange Singularities under Symplectic Reduction”, Funct. Anal. Appl., 32:1 (1998), 1–9  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. V. Goryunov, “Unitary reflection groups associated with singularities of functions with cyclic symmetry”, Russian Math. Surveys, 54:5 (1999), 873–893  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. V. M. Zakalyukin, “Simple Coisotropic Caustics”, Journal of Mathematical Sciences, 124:5 (2004), 5310–5320  mathnet  crossref  mathscinet  zmath
    8. V. V. Goryunov, V. M. Zakalyukin, “On Stability of Projections of Lagrangian Varieties”, Funct. Anal. Appl., 38:4 (2004), 249–255  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. M. Zakalyukin, A. O. Remizov, “Legendre Singularities in Systems of Implicit ODEs and Slow–Fast Dynamical Systems”, Proc. Steklov Inst. Math., 261 (2008), 136–148  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    10. V. M. Zakalyukin, A. N. Kurbatskii, “Envelope Singularities of Families of Planes in Control Theory”, Proc. Steklov Inst. Math., 262 (2008), 66–79  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    11. Proc. Steklov Inst. Math., 267 (2009), 91–103  mathnet  crossref  mathscinet  zmath  isi  elib
    12. V. M. Zakalyukin, A. N. Kurbatskii, “Convex hulls of surfaces with boundaries and corners and singularities of transitivity zone in $\mathbb R^3$”, Proc. Steklov Inst. Math., 268 (2010), 274–293  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    13. I. A. Bogaevsky, “Implicit ordinary differential equations: bifurcations and sharpening of equivalence”, Izv. Math., 78:6 (2014), 1063–1078  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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