This article is cited 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

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.

UDC: 517.987

Received: 31.05.2012

DOI: 10.4213/faa3118

 English version: Functional Analysis and Its Applications, 2013, 47:3, 174–186

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