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Mat. Sb. (N.S.), 1969, Volume 78(120), Number 3, Pages 360–373 (Mi msb3561)  

This article is cited in 20 scientific papers (total in 20 papers)

The origin of limit cycles under perturbation of the equation $\dfrac{dw}{dz}=-\dfrac{R_z}{R_w}$, where $R(z,w)$ is a polynomial

Yu. S. Ilyashenko


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English version:
Mathematics of the USSR-Sbornik, 1969, 7:3, 353–364

Bibliographic databases:

UDC: 517.9
MSC: 34C07, 34C05, 34M60
Received: 04.06.1968

Citation: Yu. S. Ilyashenko, “The origin of limit cycles under perturbation of the equation $\dfrac{dw}{dz}=-\dfrac{R_z}{R_w}$, where $R(z,w)$ is a polynomial”, Mat. Sb. (N.S.), 78(120):3 (1969), 360–373; Math. USSR-Sb., 7:3 (1969), 353–364

Citation in format AMSBIB
\Bibitem{Ily69}
\by Yu.~S.~Ilyashenko
\paper The origin of limit cycles under perturbation of the equation $\dfrac{dw}{dz}=-\dfrac{R_z}{R_w}$, where $R(z,w)$ is a~polynomial
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 78(120)
\issue 3
\pages 360--373
\mathnet{http://mi.mathnet.ru/msb3561}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=243155}
\zmath{https://zbmath.org/?q=an:0183.36501|0194.40102}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 7
\issue 3
\pages 353--364
\crossref{https://doi.org/10.1070/SM1969v007n03ABEH001094}


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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. Yu. S. Ilyashenko, “An example of eqations $\frac{dw}{dz}=\frac{P_n(z,w)}{Q_n(z,w)}$ having a countable number of limit cycles and arbitrarily large Petrovskii–Landis genus”, Math. USSR-Sb., 9:3 (1969), 365–378  mathnet  crossref  mathscinet  zmath
    2. Yu. S. Ilyashenko, “The nonalgebraic character of the manifold of differential equations with rational right-hand sides and with multiple limit cycles”, Math. USSR-Sb., 12:3 (1970), 453–457  mathnet  crossref  mathscinet  zmath
    3. Yu. S. Ilyashenko, “Algebraic nonsolvability and almost algebraic solvability of the centerfocus problem”, Funct. Anal. Appl., 6:3 (1972), 197–202  mathnet  crossref  mathscinet  zmath
    4. B. Müller, “On the density of solutions of an equation in $\mathbf{CP}^2$”, Math. USSR-Sb., 27:3 (1975), 325–338  mathnet  crossref  mathscinet  zmath
    5. Yu. S. Ilyashenko, “Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations”, Russian Math. Surveys, 40:6 (1985), 1–49  mathnet  crossref  mathscinet  adsnasa
    6. V. P. Tareev, “A complex succession function in the problem of generation of complex limit cylinders and their relation with real limit cycles”, Math. USSR-Sb., 58:1 (1987), 169–183  mathnet  crossref  mathscinet  zmath
    7. JIBIN LI, “HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS”, Int. J. Bifurcation Chaos, 13:01 (2003), 47  crossref
    8. Claire Moura, “On the multiplicity of hyperelliptic integrals”, Nonlinearity, 17:6 (2004), 2057  crossref  mathscinet  zmath  isi  elib
    9. I. A. Khovanskaya (Pushkar'), “Weak Infinitesimal Hilbert's 16th Problem”, Proc. Steklov Inst. Math., 254 (2006), 201–230  mathnet  crossref  mathscinet  elib
    10. A. A. Glutsyuk, Yu. S. Ilyashenko, “Restricted version of the infinitesimal Hilbert 16th problem”, Mosc. Math. J., 7:2 (2007), 281–325  mathnet  crossref  mathscinet  zmath
    11. Weigu Li, Jaume Llibre, Jiazhong Yang, Zhifen Zhang, “Limit Cycles Bifurcating from the Period Annulus of Quasi-Homogeneous Centers”, J Dyn Diff Equat, 2008  crossref  isi
    12. Hossein Movasati, “On elliptic modular foliations”, Indagationes Mathematicae, 19:2 (2008), 263  crossref
    13. Hossein Movasati, Evilson Vieira, “Projective limit cycles”, Mosc. Math. J., 9:4 (2009), 855–866  mathnet  crossref  mathscinet  zmath
    14. C. Christopher, P. Mardešic, “The Monodromy Problem and the Tangential Center Problem”, Funct. Anal. Appl., 44:1 (2010), 22–35  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Maoan Han, Jibin Li, “Lower bounds for the Hilbert number of polynomial systems”, Journal of Differential Equations, 2011  crossref
    16. Cherkas L.A., “Predelnye tsikly pri vozmuschenii kvadratichnogo tsentra s simmetriei”, Differentsialnye uravneniya, 47:8 (2011), 1067–1076  elib
    17. Salomón Rebollo-Perdomo, “Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to”, Journal of Mathematical Analysis and Applications, 2012  crossref
    18. A. Álvarez, J. L. Bravo, P. Mardešić, “Inductive solution of the tangential center problem on zero-cycles”, Mosc. Math. J., 13:4 (2013), 555–583  mathnet  crossref  mathscinet
    19. Jian-ping Shi, Ji-bin Li, “Bifurcations of limit cycles in a <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:msub><mml:mrow><mml:mi>Z</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-equivariant planar vector field of degree 7”, Applied Mathematics and Computation, 244 (2014), 191  crossref
    20. Pavao Mardešić, Dmitry Novikov, Laura Ortiz-Bobadilla, Jessie Pontigo-Herrera, “Bounding the length of iterated integrals of the first nonzero Melnikov function”, Mosc. Math. J., 18:2 (2018), 367–386  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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