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Izvestiya: Mathematics, 2016, Volume 80, Issue 1, Pages 50–112
DOI: https://doi.org/10.1070/IM8352 (Mi im8352) 		 
This article is cited in 3 scientific papers (total in 3 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
English version PDF (745 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM8352
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).
Received: 03.02.2015
Revised: 29.08.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2016, Volume 80, Issue 1, Pages 55–118
DOI: https://doi.org/10.4213/im8352
Bibliographic databases:
Document Type: Article
UDC: 517.925
MSC: 37F75
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM8352
  • https://www.mathnet.ru/eng/im/v80/i1/p55
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1046
    Russian version PDF:362
    English version PDF:39
    References:121
    First page:111
     
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