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Dokl. Akad. Nauk SSSR, 1981, Volume 260, Number 1, Pages 31–35 (Mi dan44681)  

This article is cited in 28 scientific papers (total in 28 papers)

MATHEMATICS

Multivalued functions and functionals. An analogue of the Morse theory

S. P. Novikov

Landau Institute for Theoretical Physics, USSR Academy of Sciences, Chernogolovka Moscow region

Full text: PDF file (677 kB)

Bibliographic databases:
UDC: 513.835
Received: 08.04.1981

Citation: S. P. Novikov, “Multivalued functions and functionals. An analogue of the Morse theory”, Dokl. Akad. Nauk SSSR, 260:1 (1981), 31–35

Citation in format AMSBIB
\Bibitem{Nov81}
\by S.~P.~Novikov
\paper Multivalued functions and functionals. An analogue of the Morse theory
\jour Dokl. Akad. Nauk SSSR
\yr 1981
\vol 260
\issue 1
\pages 31--35
\mathnet{http://mi.mathnet.ru/dan44681}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0630459}
\zmath{https://zbmath.org/?q=an:0505.58011}


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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. S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. S. P. Novikov, “The analytic generalized Hopf invariant. Many-valued functionals”, Russian Math. Surveys, 39:5 (1984), 113–124  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. L. D. Faddeev, S. L. Shatashvili, “Algebraic and Hamiltonian methods in the theory of non-Abelian anomalies”, Theoret. and Math. Phys., 60:2 (1984), 770–778  mathnet  crossref  mathscinet  isi
    4. M. Sh. Farber, “Exactness of the Novikov inequalities”, Funct. Anal. Appl., 19:1 (1985), 40–48  mathnet  crossref  mathscinet  zmath  isi
    5. E. A. Ivanov, S. O. Krivonos, “$N=4$ superextension of the Liouville equation with quaternion structure”, Theoret. and Math. Phys., 63:2 (1985), 477–486  mathnet  crossref  mathscinet  isi
    6. I. V. Volovich, “Supersymmetric chiral field with anomaly and its integrability”, Theoret. and Math. Phys., 63:2 (1985), 533–535  mathnet  crossref  mathscinet  isi
    7. E. A. Ivanov, S. O. Krivonos, “Bäcklund transformations for superextensions of the Liouville equation”, Theoret. and Math. Phys., 66:1 (1986), 60–68  mathnet  crossref  mathscinet  zmath  isi
    8. A. V. Zorich, “The quasiperiodic structure of level surfaces of a Morse 1-form close to a rational one – a problem of S. P. Novikov”, Math. USSR-Izv., 31:3 (1988), 635–655  mathnet  crossref  mathscinet  zmath
    9. E. A. Ivanov, “Duality in $d=2$ $\sigma$ models of chiral field with anomaly”, Theoret. and Math. Phys., 71:2 (1987), 474–484  mathnet  crossref  mathscinet  isi
    10. E. A. Ivanov, A. P. Isaev, “The Green–Schwarz superstring as an asymmetric model of a chiral field”, Theoret. and Math. Phys., 81:3 (1989), 1304–1313  mathnet  crossref  mathscinet  isi
    11. S. V. Talalov, “Current algebras in the theory of the classical $\mathcal D=2+1$ string with internal degrees of freedom”, Theoret. and Math. Phys., 79:1 (1989), 369–374  mathnet  crossref  mathscinet  isi
    12. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. S. V. Talalov, “Spinning string in four-dimensional spacetime as a model of $SL(2,\mathbb C)$ chiral field with anomaly. I”, Theoret. and Math. Phys., 82:2 (1990), 139–145  mathnet  crossref  mathscinet  zmath  isi
    14. Yu. P. Solov'ev, “The topology of four-dimensional manifolds”, Russian Math. Surveys, 46:2 (1991), 167–232  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. I. A. Taimanov, “Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals”, Math. USSR-Izv., 38:2 (1992), 359–374  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. I. A. Taimanov, “Closed extremals on two-dimensional manifolds”, Russian Math. Surveys, 47:2 (1992), 163–211  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. S. V. Talalov, “String dynamics in $D=4$ space-time I. Hamiltonian formalism”, Theoret. and Math. Phys., 106:2 (1996), 182–194  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. A. V. Pajitnov, “Simple homotopy type of the Novikov complex and the Lefschetz $\zeta$-function of a gradient flow”, Russian Math. Surveys, 54:1 (1999), 119–169  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. S. V. Talalov, “Geometric description of a relativistic string”, Theoret. and Math. Phys., 123:1 (2000), 446–450  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. D. V. Millionshchikov, “Cohomology of solvable lie algebras and solvmanifolds”, Math. Notes, 77:1 (2005), 61–71  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    21. St. Petersburg Math. J., 18:5 (2007), 809—835  mathnet  crossref  mathscinet  zmath  elib
    22. M. Farber, D. Schütz, “Novikov–Betti numbers and the fundamental group”, Russian Math. Surveys, 61:6 (2006), 1173–1175  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. E. I. Yakovlev, “Bundles and Geometric Structures Associated With Gyroscopic Systems”, Journal of Mathematical Sciences, 153:6 (2008), 828–855  mathnet  crossref  mathscinet  zmath  elib
    24. S. V. Talalov, “$N$-soliton strings in four-dimensional space–time”, Theoret. and Math. Phys., 152:3 (2007), 1234–1242  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. M. Farber, D. Schütz, “Closed 1-forms in topology and dynamics”, Russian Math. Surveys, 63:6 (2008), 1079–1139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. M. Farber, R. Geoghegan, D. Schütz, “Closed 1-forms in topology and geometric group theory”, Russian Math. Surveys, 65:1 (2010), 143–172  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. St. Petersburg Math. J., 26:3 (2015), 441–461  mathnet  crossref  mathscinet  isi  elib
    28. H. Itoyama, A. D. Mironov, A. Yu. Morozov, “Matching branches of a nonperturbative conformal block at its singularity divisor”, Theoret. and Math. Phys., 184:1 (2015), 891–923  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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