Geodesic
Saddle connections
Sbornik. Mathematics, Tome 215 (2024) no. 11, pp. 1523-1548

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that vector fields that are close to a fixed field with the same set of connections form a smooth Banach submanifold. A sufficient condition for the birth of saddle connections in a generic family is presented. The following result is proved: in a perturbation of a monodromic hyperbolic polycycle of $n$ connections in a generic family at least $n$ limit cycles can appear. Bibliography: 21 titles.
Keywords: separatrix connections, cyclicity.
Mots-clés : limit cycles, polycycles 
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     author = {A. V. Dukov},
     title = {Saddle connections},
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A. V. Dukov. Saddle connections. Sbornik. Mathematics, Tome 215 (2024) no. 11, pp. 1523-1548. http://geodesic.mathdoc.fr/item/SM_2024_215_11_a3/