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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
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.
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
Linking options:
https://www.mathnet.ru/eng/mmj742 https://www.mathnet.ru/eng/mmj/v19/i4/p709
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Abstract page: | 214 | References: | 31 |
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