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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 3, Pages 12–27
DOI: https://doi.org/10.4213/faa3118 (Mi faa3118) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the Number of Limit Cycles Which Appear by Perturbation of Two-Saddle Cycles of Planar Vector Fields

L. Gavrilov

Institute de Mathématique de Toulouse
Full-text PDF (411 kB) Citations (5)
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DOI: https://doi.org/10.4213/faa3118
Abstract: We prove that the number of limit cycles which bifurcate from a two-saddle loop of an analytic planar vector field $X_0$ under an arbitrary finite-parameter analytic deformation $X_\lambda$, $\lambda\in(\mathbb{R}^N,0)$, is uniformly bounded with respect to $\lambda$.
Keywords: limit cycles, finite cyclicity, heteroclinic loop, two-saddle loop.
Received: 31.05.2012
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 3, Pages 174–186
DOI: https://doi.org/10.1007/s10688-013-0024-x
Bibliographic databases:
Document Type: Article
UDC: 517.987
Language: Russian
Citation: L. Gavrilov, “On the Number of Limit Cycles Which Appear by Perturbation of Two-Saddle Cycles of Planar Vector Fields”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 12–27; Funct. Anal. Appl., 47:3 (2013), 174–186
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa3118
  • https://doi.org/10.4213/faa3118
  • https://www.mathnet.ru/eng/faa/v47/i3/p12
    • This publication is cited in the following 5 articles:
    1. Gavrilov L., Gargouri A., Ben Hamed B., “Special Cubic Perturbations of the Duffing Oscillator X ‘’ = X - X(3) Near the Eight-Loop”, Mediterr. J. Math., 18:6 (2021), 229  crossref  mathscinet  isi
    2. Geng W. Tian Yu., “Bifurcation of Limit Cycles Near Heteroclinic Loops in Near-Hamiltonian Systems”, Commun. Nonlinear Sci. Numer. Simul., 95 (2021), 105666  crossref  mathscinet  isi
    3. Gavrilov L., Iliev I.D., “Cubic Perturbations of Elliptic Hamiltonian Vector Fields of Degree Three”, J. Differ. Equ., 260:5 (2016), 3963–3990  crossref  mathscinet  zmath  isi  scopus
    4. Caubergh M., “Bifurcation of the Separatrix Skeleton in Some 1-Parameter Families of Planar Vector Fields”, J. Differ. Equ., 259:3 (2015), 989–1013  crossref  mathscinet  zmath  isi  elib  scopus
    5. Gavrilov L., They I.D., “Perturbations of Quadratic Hamiltonian Two-Saddle Cycles”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 32:2 (2015), 307–324  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:567
    Full-text PDF :219
    References:80
    First page:21
     
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