Geodesic
Finiteness theorems for limit cycles: a digest of the revised proof
Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 50-112

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This is the first paper in a series of two presenting a digest of the proof of the finiteness theorem for limit cycles of a planar polynomial vector field. At the same time we sketch the proof of the following two theorems: an analogous result for analytic vector fields, and a description of the asymptotics of the monodromy transformation for polycycles of such fields.
Keywords: elementary polycycles, superexact asymptotic series.
Mots-clés : limit cycles, functional cochains 
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Yu. S. Ilyashenko. Finiteness theorems for limit cycles: a digest of the revised proof. Izvestiya. Mathematics , Tome 80 (2016) no. 1, pp. 50-112. http://geodesic.mathdoc.fr/item/IM2_2016_80_1_a3/