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Regular version of the site

Article

Finiteness theorems for limit cycles: A digest of the revised proof

Izvestiya. Mathematics. 2016. Vol. 80. No. 1. P. 50-112.

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. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.