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Algebra i Analiz, 2010, Volume 22, Issue 4, Pages 57–75 (Mi aa1197)  
This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Cyclicity of elementary polycycles with fixed number of singular points in generic k-parameter families

P. I. Kaleda, I. V. Shchurov

M. V. Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (375 kB) Citations (3)
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Abstract: An estimate is found for the number of limit cycles arising from polycycles in generic finite-parameter families of differential equations on the two-sphere. It is proved that if the polycycles have a fixed number of singular points and all the singular points are elementary, then an estimate of cyclicity holds true, which is polynomial in the number of parameters of the family.
Keywords: number of limit cycles, polycycle, Hilbert's sixteenth problem, Hilbert–Arnol'd problem.
Received: 05.07.2009
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 4, Pages 557–571
DOI: https://doi.org/10.1090/S1061-0022-2011-01158-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. I. Kaleda, I. V. Shchurov, “Cyclicity of elementary polycycles with fixed number of singular points in generic k-parameter families”, Algebra i Analiz, 22:4 (2010), 57–75; St. Petersburg Math. J., 22:4 (2011), 557–571
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1197
  • https://www.mathnet.ru/eng/aa/v22/i4/p57
    • This publication is cited in the following 3 articles:
    1. A. V. Dukov, “Saddle connections”, Sb. Math., 215:11 (2024), 1523–1548  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. A. V. Dukov, “Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles”, Sb. Math., 214:2 (2023), 226–245  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Ilyashenko Y., “Towards the General Theory of Global Planar Bifurcations”, Mathematical Sciences With Multidisciplinary Applications: in Honor of Professor Christiane Rousseau. and in Recognition of the Mathematics For Planet Earth Initiative, Springer Proceedings in Mathematics & Statistics, 157, ed. Toni B., Springer, 2016, 269–299  crossref  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Full-text PDF :124
    References:56
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