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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 12–27 (Mi faa3118)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.4213/faa3118

Full text: PDF file (411 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 174–186

Bibliographic databases:

UDC: 517.987
Received: 31.05.2012

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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    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. 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
    2. 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
    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
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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