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Moscow Mathematical Journal, 2019, Volume 19, Number 4, Pages 709–737
DOI: https://doi.org/10.17323/1609-4514-2019-19-4-709-737 (Mi mmj742) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$

N. Goncharuka, Yu. Ilyashenkobc, N. Solodovnikovd

a Department Of Mathematical and Computational Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Deerfield Hall, 3008K, Mississauga, On L5L 1C6
b National Research University Higher School of Economics, Russia
c Independent University of Moscow
d Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St., Moscow 119991, Russia
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DOI: https://doi.org/10.17323/1609-4514-2019-19-4-709-737
Abstract: We classify global bifurcations in generic one-parameter local families of vector fields on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in monographs on the bifurcation theory. As a by product we prove that generic families described above are structurally stable.
Key words and phrases: bifurcation, polycycle, structural stability, sparkling saddle connection.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00748-a
The authors were supported in part by the grant RFBR 16-01-00748-a and Laboratory Poncelet.
Bibliographic databases:
Document Type: Article
MSC: 34C23, 37G99, 37E35
Language: English
Citation: N. Goncharuk, Yu. Ilyashenko, N. Solodovnikov, “Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$”, Mosc. Math. J., 19:4 (2019), 709–737
Citation in format AMSBIB
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\by N.~Goncharuk, Yu.~Ilyashenko, N.~Solodovnikov
\paper Global bifurcations in generic one-parameter families with a parabolic cycle on $S^2$
\jour Mosc. Math.~J.
\yr 2019
\vol 19
\issue 4
\pages 709--737
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