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. 
@article{FAA_2013_47_3_a1,
     author = {L. Gavrilov},
     title = {On the {Number} of {Limit} {Cycles} {Which} {Appear} by {Perturbation} of {Two-Saddle} {Cycles} of {Planar} {Vector} {Fields}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {12--27},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a1/}
}
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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/