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

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

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.


DOI: https://doi.org/10.17323/1609-4514-2019-19-4-709-737

Full text: http://www.mathjournals.org/.../2019-019-004-004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 34C23, 37G99, 37E35
Language:

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
\Bibitem{GonIlySol19}
\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
\mathnet{http://mi.mathnet.ru/mmj742}
\crossref{https://doi.org/10.17323/1609-4514-2019-19-4-709-737}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4037812}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074719137}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Nataliya Goncharuk, Yury Kudryashov, “Bifurcations of the polycycle “tears of the heart”: multiple numerical invariants”, Mosc. Math. J., 20:2 (2020), 323–341  mathnet  crossref
    2. N. B. Goncharuk, Yu. S. Ilyashenko, “Various Equivalence Relations in Global Bifurcation Theory”, Proc. Steklov Inst. Math., 310 (2020), 78–97  mathnet  crossref  crossref  mathscinet  isi  elib
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