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Funktsional. Anal. i Prilozhen., 1971, Volume 5, Issue 3, Pages 1–9 (Mi faa2590)  

This article is cited in 30 scientific papers (total in 32 papers)

Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms

V. I. Arnol'd

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English version:
Functional Analysis and Its Applications, 1971, 5:3, 169–176

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Received: 22.03.1971

Citation: V. I. Arnol'd, “Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms”, Funktsional. Anal. i Prilozhen., 5:3 (1971), 1–9; Funct. Anal. Appl., 5:3 (1971), 169–176

Citation in format AMSBIB
\by V.~I.~Arnol'd
\paper Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms
\jour Funktsional. Anal. i Prilozhen.
\yr 1971
\vol 5
\issue 3
\pages 1--9
\jour Funct. Anal. Appl.
\yr 1971
\vol 5
\issue 3
\pages 169--176

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    This publication is cited in the following articles:
    1. V. A. Rokhlin, “Proof of Gudkov's hypothesis”, Funct. Anal. Appl., 6:2 (1972), 136–138  mathnet  crossref  mathscinet  zmath
    2. V. A. Rokhlin, “Congruences modulo 16 in Hilbert's sixtieth problem”, Funct. Anal. Appl., 6:4 (1972), 301–306  mathnet  crossref  mathscinet  zmath
    3. D. A. Gudkov, “The topology of real projective algebraic varieties”, Russian Math. Surveys, 29:4 (1974), 1–79  mathnet  crossref  mathscinet  zmath
    4. V. M. Kharlamov, “The topological type of nonsingular surfaces in $\mathbb{RP}^3$ of degree four”, Funct. Anal. Appl., 10:4 (1976), 295–305  mathnet  crossref  mathscinet  zmath
    5. V. A. Rokhlin, “Complex topological characteristics of real algebraic curves”, Russian Math. Surveys, 33:5 (1978), 85–98  mathnet  crossref  mathscinet  zmath
    6. V. I. Arnol'd, “Critical points of functions on a manifold with boundary, the simple Lie groups $B_k$, $C_k$, and $F_4$ and singularities of evolutes”, Russian Math. Surveys, 33:5 (1978), 99–116  mathnet  crossref  mathscinet  zmath
    7. 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
    8. V. I. Zvonilov, “Refinement of the Petrovskii–Arnol'd inequality for curves of odd degree”, Funct. Anal. Appl., 13:4 (1979), 262–268  mathnet  crossref  mathscinet  zmath
    9. V. A. Rokhlin, “New inequalities in the topology of real planar algebraic curves”, Funct. Anal. Appl., 14:1 (1980), 29–33  mathnet  crossref  mathscinet  zmath
    10. V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172  mathnet  crossref  mathscinet  zmath
    11. O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Russian Math. Surveys, 41:3 (1986), 55–82  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. A. B. Korchagin, E. I. Shustin, “Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point”, Math. USSR-Izv., 33:3 (1989), 501–520  mathnet  crossref  mathscinet  zmath
    13. E. I. Shustin, “New restrictions on the topology of real curves of degree a multiple of 8”, Math. USSR-Izv., 37:2 (1991), 421–443  mathnet  crossref  mathscinet  zmath  adsnasa
    14. V. A. Krasnov, “Characteristic classes of vector bundles on a real algebraic variety”, Math. USSR-Izv., 39:1 (1992), 703–730  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. V. A. Krasnov, “On cohomology classes defined by the real points of a real algebraic $\operatorname{GM}$-surface”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 385–395  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. V. A. Krasnov, “Algebraic cycles on a real algebraic GM-manifold and their applications”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 141–160  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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. V. A. Krasnov, “Real algebraic GM-varieties”, Izv. Math., 62:3 (1998), 465–491  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. V. I. Arnol'd, “Relatives of the Quotient of the Complex Projective Plane by the Complex Conjugation”, Proc. Steklov Inst. Math., 224 (1999), 46–56  mathnet  mathscinet  zmath
    20. 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
    21. 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
    22. Orevkov, SY, “Flexible, algebraically unrealizable curves: rehabilitation of Hilbert-Rohn-Gudkov approach”, Journal fur Die Reine und Angewandte Mathematik, 551 (2002), 145  isi
    23. S. Yu. Orevkov, E. I. Shustin, “Pseudoholomorphic algebraically unrealizable curves”, Mosc. Math. J., 3:3 (2003), 1053–1083  mathnet  mathscinet  zmath
    24. I. O. Kalinin, “On the cohomology of real algebraic varieties”, J. Math. Sci. (N. Y.), 131:1 (2005), 5323–5344  mathnet  crossref  mathscinet  zmath  elib
    25. Li, JB, “Hilbert's 16th problem and bifurcations of planar polynomial vector fields”, International Journal of Bifurcation and Chaos, 13:1 (2003), 47  crossref  isi
    26. V. A. Krasnov, “The Nikulin Congruence for Four-Dimensional $M$-Varieties”, Math. Notes, 76:2 (2004), 191–199  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    27. V. A. Krasnov, “Rigid isotopy classification of real three-dimensional cubics”, Izv. Math., 70:4 (2006), 731–768  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. Brugalle, E, “Symmetric plane curves of degree 7: pseudoholomorphic and algebraic classifications”, Journal fur Die Reine und Angewandte Mathematik, 612 (2007), 129  isi
    29. V. I. Arnold, “Topological properties of eigenoscillations in mathematical physics”, Proc. Steklov Inst. Math., 273 (2011), 25–34  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    30. G. M. Polotovskii, “V. V. Morozov, D. A. Gudkov i pervaya chast $16$-i problemy Gilberta”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 31–43  mathnet
    31. V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139  mathnet  crossref  crossref  adsnasa  isi  elib
    32. V. A. Krasnov, “On a classical correspondence of real K3 surfaces”, Izv. Math., 82:4 (2018), 662–693  mathnet  crossref  crossref  adsnasa  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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