Geodesic
On the Number of Limit Cycles Which Appear by Perturbation of Two-Saddle Cycles of Planar Vector Fields
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 12-27.

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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 $\lambda$.
Mots-clés : limit cycles
Keywords: finite cyclicity, heteroclinic loop, two-saddle loop. 
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L. Gavrilov. On the Number of Limit Cycles Which Appear by Perturbation of Two-Saddle Cycles of Planar Vector Fields. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 12-27. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a1/

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