Matematicheskii Sbornik. Novaya Seriya
General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

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

This article is cited in 21 scientific papers (total in 21 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

Full text: PDF file (1435 kB)
References: PDF file   HTML file

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
\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
\jour Math. USSR-Sb.
\yr 1969
\vol 7
\issue 3
\pages 353--364

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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  mathscinet  zmath
    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  mathscinet  isi
    12. Hossein Movasati, “On elliptic modular foliations”, Indagationes Mathematicae, 19:2 (2008), 263  crossref  mathscinet  zmath
    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  mathscinet
    16. Cherkas L.A., “Predelnye tsikly pri vozmuschenii kvadratichnogo tsentra s simmetriei”, Differentsialnye uravneniya, 47:8 (2011), 1067–1076  mathscinet  zmath  elib
    17. Salomón Rebollo-Perdomo, “Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to”, Journal of Mathematical Analysis and Applications, 2012  crossref  mathscinet
    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="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals="" xmlns:sa=""><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  mathscinet  zmath
    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
    21. A. Alvares, Kh. L. Bravo, K. Kristofer, P. Mardeshich, “Infinitezimalnaya problema tsentra na nulevykh tsiklakh i gipoteza kompozitsii”, Funkts. analiz i ego pril., 55:4 (2021), 3–21  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:745
    Full text:145
    First page:2

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021