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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 1, Pages 55–118 (Mi izv8352)  

This article is cited in 2 scientific papers (total in 2 papers)

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

Yu. S. Ilyashenkoabc

a Independent University of Moscow
b Cornell University
c National Research University "Higher School of Economics", Moscow

Abstract: 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: limit cycles, elementary polycycles, functional cochains, superexact asymptotic series.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00969
The author was supported in part by the RFBR (grant no. 13-01-00969).


DOI: https://doi.org/10.4213/im8352

Full text: PDF file (1058 kB)
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English version:
Izvestiya: Mathematics, 2016, 80:1, 50–112

Bibliographic databases:

UDC: 517.925
MSC: 37F75
Received: 03.02.2015
Revised: 29.08.2015

Citation: Yu. S. Ilyashenko, “Finiteness theorems for limit cycles: a digest of the revised proof”, Izv. RAN. Ser. Mat., 80:1 (2016), 55–118; Izv. Math., 80:1 (2016), 50–112

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    This publication is cited in the following articles:
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    2. R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Sb. Math., 210:9 (2019), 1207–1221  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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