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Funktsional. Anal. i Prilozhen., 1978, Volume 12, Issue 1, Pages 1–14 (Mi faa1957)  

This article is cited in 24 scientific papers (total in 26 papers)

Index of a singular point of a vector field, the Petrovskii–Oleinik inequality, and mixed hodge structures

V. I. Arnol'd


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English version:
Functional Analysis and Its Applications, 1978, 12:1, 1–12

Bibliographic databases:

UDC: 513.60+517.9
Received: 06.09.1977

Citation: V. I. Arnol'd, “Index of a singular point of a vector field, the Petrovskii–Oleinik inequality, and mixed hodge structures”, Funktsional. Anal. i Prilozhen., 12:1 (1978), 1–14; Funct. Anal. Appl., 12:1 (1978), 1–12

Citation in format AMSBIB
\Bibitem{Arn78}
\by V.~I.~Arnol'd
\paper Index of a singular point of a vector field, the Petrovskii--Oleinik inequality, and mixed hodge structures
\jour Funktsional. Anal. i Prilozhen.
\yr 1978
\vol 12
\issue 1
\pages 1--14
\mathnet{http://mi.mathnet.ru/faa1957}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=498592}
\zmath{https://zbmath.org/?q=an:0398.57031|0407.57025}
\transl
\jour Funct. Anal. Appl.
\yr 1978
\vol 12
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1007/BF01077558}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Nikulin, “Integral symmetric bilinear forms and some of their applications”, Math. USSR-Izv., 14:1 (1980), 103–167  mathnet  crossref  mathscinet  zmath  isi
    2. A. G. Khovanskii, “Index of a polynomial field”, Funct. Anal. Appl., 13:1 (1979), 38–45  mathnet  crossref  mathscinet  zmath
    3. A. N. Varchenko, “A formula for the ranks of the homology groups of the boundary of an isolated singularity of a surface in $\mathbb{C}^3$ and the Newton diagram”, Funct. Anal. Appl., 13:1 (1979), 52–53  mathnet  crossref  mathscinet  zmath
    4. V. I. Danilov, “Newton polyhedra and vanishing cohomology”, Funct. Anal. Appl., 13:2 (1979), 103–115  mathnet  crossref  mathscinet  zmath
    5. F. S. Berezovskaya, “Index of a stationary point of a vector field on the plane”, Funct. Anal. Appl., 13:2 (1979), 137–137  mathnet  crossref  mathscinet  zmath
    6. A. N. Varchenko, “Asymptotic Hodge structure in the vanishing cohomology”, Math. USSR-Izv., 18:3 (1982), 469–512  mathnet  crossref  mathscinet  zmath
    7. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi
    8. A. N. Varchenko, “The complex exponent of a singularity does not change along strata $\mu=\mathrm{const}$”, Funct. Anal. Appl., 16:1 (1982), 1–9  mathnet  crossref  mathscinet  zmath  isi
    9. V. I. Arnol'd, “Singularities of systems of rays”, Russian Math. Surveys, 38:2 (1983), 87–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. S. M. Gusein-Zade, “Index of a singular point of a gradient vector field”, Funct. Anal. Appl., 18:1 (1984), 6–10  mathnet  crossref  mathscinet  zmath  isi
    11. A. N. Varchenko, “On the local residue and the intersection form on the vanishing cohomology”, Math. USSR-Izv., 26:1 (1986), 31–52  mathnet  crossref  mathscinet  zmath
    12. V. A. Krasnov, “Degenerations of real algebraic varieties”, Math. USSR-Izv., 27:1 (1986), 115–140  mathnet  crossref  mathscinet  zmath
    13. V. N. Karpushkin, “Precise order bounds for the number of components of the complement of the zeros of harmonic polynomials”, Funct. Anal. Appl., 19:4 (1985), 295–299  mathnet  crossref  mathscinet  zmath  isi
    14. V. N. Karpushkin, “Topology of the zeros of eigenfunctions”, Funct. Anal. Appl., 23:2 (1989), 218–220  mathnet  crossref  mathscinet  zmath  isi
    15. V. N. Karpushkin, “Bounds for the Betti numbers of a level surface of a harmonic polynomial”, Funct. Anal. Appl., 26:4 (1992), 300–302  mathnet  crossref  mathscinet  zmath  isi
    16. V. N. Karpushkin, “The number of components of complements to level surfaces of partially harmonic polynomials”, Math. Notes, 62:6 (1997), 697–700  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    18. X. Gomez-Mont, P. Mardešic, “Index of a Vector Field Tangent to an Odd-Dimensional Hypersurface and the Signature of the Relative Hessian”, Funct. Anal. Appl., 33:1 (1999), 1–10  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. Gonzalez-Ramirez, JA, “Deformations of functions without real critical points”, Communications in Algebra, 31:9 (2003), 4255  crossref  isi
    22. T. M. Aliashvili, G. N. Khimshiashvili, “On the Euler characteristic of an intersection of quadrics”, Russian Math. Surveys, 61:3 (2006), 551–552  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. Giraldo, L, “Flags in zero dimensional complete intersection algebras and indices of real vector fields”, Mathematische Zeitschrift, 260:1 (2008), 77  crossref  isi
    24. Brasselet, JP, “The Case of Manifolds”, Vector Fields on Singular Varieties, 1987 (2009), 1  crossref  isi
    25. Cisneros-Molina J.L., Seade J., Grulha Jr. Nivaldo G., “On the Topology of Real Analytic Maps”, Int. J. Math., 25:7 (2014), 1450069  crossref  isi
    26. Seade J., “On Milnor'S Fibration Theorem and Its Offspring After 50 Years”, Bull. Amer. Math. Soc., 56:2 (2019), 281–348  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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