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JOURNALS // Moscow Mathematical Journal // Archive

Mosc. Math. J., 2019 Volume 19, Number 4, Pages 709–737 (Mi mmj742)

This article is cited 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.

MSC: 34C23, 37G99, 37E35

Language: English

DOI: 10.17323/1609-4514-2019-19-4-709-737



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