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Uspekhi Mat. Nauk, 1985, Volume 40, Issue 6(246), Pages 41–78 (Mi umn2786)  

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

Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations

Yu. S. Ilyashenko


Full text: PDF file (5417 kB)
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English version:
Russian Mathematical Surveys, 1985, 40:6, 1–49

Bibliographic databases:

UDC: 517.9
MSC: 34C07, 34M35, 34M60, 34Exx
Received: 02.03.1983

Citation: Yu. S. Ilyashenko, “Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations”, Uspekhi Mat. Nauk, 40:6(246) (1985), 41–78; Russian Math. Surveys, 40:6 (1985), 1–49

Citation in format AMSBIB
\Bibitem{Ily85}
\by Yu.~S.~Ilyashenko
\paper Dulac's memoir ``On limit cycles'' and related problems of the local theory of differential equations
\jour Uspekhi Mat. Nauk
\yr 1985
\vol 40
\issue 6(246)
\pages 41--78
\mathnet{http://mi.mathnet.ru/umn2786}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=815489}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1985RuMaS..40....1I}
\transl
\jour Russian Math. Surveys
\yr 1985
\vol 40
\issue 6
\pages 1--49
\crossref{https://doi.org/10.1070/RM1985v040n06ABEH003701}


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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. V. S. Samovol, “On smooth linearization of systems of differential equations in a neighbourhood of a saddle singular point”, Russian Math. Surveys, 43:4 (1988), 231–232  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. J Guckenheimer, R Rand, D Schlomiuk, Nonlinearity, 2:3 (1989), 405  crossref  mathscinet  zmath  adsnasa  isi
    3. Yang Kuang, “Finiteness of limit cycles in planar autonomous systems”, Applicable Analysis, 32:3-4 (1989), 253  crossref
    4. Yu. S. Ilyashenko, “Finiteness theorems for limit cycles”, Russian Math. Surveys, 45:2 (1990), 129–203  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. I. Trifonov, “Divergence of Dulac's rows”, Math. USSR-Sb., 69:1 (1991), 37–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Yu. S. Ilyashenko, S. Yu. Yakovenko, “Finitely-smooth normal forms of local families of diffeomorphisms and vector fields”, Russian Math. Surveys, 46:1 (1991), 1–43  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Steve Smale, “Dynamics retrospective: great problems, attempts that failed”, Physica D: Nonlinear Phenomena, 51:1-3 (1991), 267  crossref
    8. Massimo Villarini, “regularity properties of the period function near a center of a planar vector field”, Nonlinear Analysis: Theory, Methods & Applications, 19:8 (1992), 787  crossref
    9. N. B. Medvedeva, “Asimptotika preobrazovaniya monodromii slozhnoi monodromnom osoboi tochki”, Vestnik ChelGU, 1994, no. 2, 68–79  mathnet
    10. A. A. Davydov, L. Ortiz-Bobadilla, “Smooth normal forms of folded elementary singular points”, J Dyn Control Syst, 1:4 (1995), 463  crossref  mathscinet  zmath  elib
    11. Marcello Galeotti, “Monodromic unbounded polycycles”, Annali di Matematica, 171:1 (1996), 83  crossref  mathscinet  zmath  isi
    12. Rudolf Winkel, “An Exponential Formula for Polynomial Vector Fields”, Advances in Mathematics, 128:1 (1997), 190  crossref
    13. Steve Smale, “Mathematical problems for the next century”, Math Intelligencer, 20:2 (1998), 7  crossref  mathscinet  zmath  isi
    14. Dumortier F., Ilyashenko Y., Rousseau C., “Normal Forms Near a Saddle-Node and Applications to Finite Cyclicity of Graphics”, Ergod. Theory Dyn. Syst., 22:Part 3 (2002), 783–818  crossref  isi
    15. Ilyashenko Y., “Centennial History of Hilbert's 16th Problem”, Bull. Amer. Math. Soc., 39:3 (2002), 301–354  crossref  isi
    16. N. B. Medvedeva, “Problema razlicheniya tsentra i fokusa v klasse rostkov s dvumya rebrami diagrammy Nyutona”, Vestnik ChelGU, 2003, no. 9, 86–110  mathnet
    17. N. B. Medvedeva, “On the Analytic Solvability of the Problem of Distinguishing between Center and Focus”, Proc. Steklov Inst. Math., 254 (2006), 7–93  mathnet  crossref  mathscinet  elib
    18. Kleptsyn, V, “An example of non-coincidence of minimal and statistical attractors”, Ergodic Theory and Dynamical Systems, 26 (2006), 759  crossref  mathscinet  zmath  isi  elib
    19. T. I. Golenishcheva-Kutuzova, V. A. Kleptsyn, “Convergence of the Krylov–Bogolyubov Procedure in Bowan's Example”, Math. Notes, 82:5 (2007), 608–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib
    21. R.D.. Costin, “The Return Map for a Planar Vector Field with Nilpotent Linear Part: A Direct and Explicit Derivation”, International Journal of Mathematics and Mathematical Sciences, 2009 (2009), 1  crossref
    22. R.D.. COSTIN, “EXPLICIT DERIVATION OF RETURN MAPS FOR PLANAR VECTOR FIELDS WITH NILPOTENT LINEAR PART WITH A CENTER OR A FOCUS”, Anal. Appl, 2012, 1350011  crossref
    23. A. S. Voronin, N. B. Medvedeva, “Asymptotics of the monodromy transformation in certain classes of monodromy germs”, Izv. Math., 77:2 (2013), 253–270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. N. B. Medvedeva, “On analytic insolubility of the stability problem on the plane”, Russian Math. Surveys, 68:5 (2013), 923–949  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    25. Leonov G.A. Kuznetsov N.V., “Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits”, Int. J. Bifurcation Chaos, 23:1 (2013), 1330002  crossref  isi
    26. Yu. S. Ilyashenko, “Finiteness theorems for limit cycles: a digest of the revised proof”, Izv. Math., 80:1 (2016), 50–112  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. N. B. Medvedeva, “Asimptoticheskoe razlozhenie preobrazovaniya monodromii”, Chelyab. fiz.-matem. zhurn., 1:1 (2016), 59–72  mathnet  elib
    28. N. B. Medvedeva, M. A. Sosnovskaya, “Vychislenie koeffitsientov stepennogo ryada preobrazovaniya monodromii v sisteme Maple”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 181–192  mathnet  mathscinet  elib
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