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Tr. Mosk. Mat. Obs., 2018, Volume 79, Issue 2, Pages 247–269 (Mi mmo615)  

Bifurcations of the ‘heart’ polycycle in generic 2-parameter families

A. V. Dukovab

a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
b Department of Mathematics, National Research University "Higher School of Economics", Moscow

Abstract: The paper concerns the ‘heart’ polycycle. We show that the set of vector fields containing a ‘heart’ polycycle form a Banach submanifold of codimension two in the space of smooth vector fields on a two-dimensional sphere. The bifurcation diagram of a generic family containing such a polycycle is constructed and surgery on the phase portrait is described.

Key words and phrases: polycycle, two-parameter family, bifurcation diagram, sparkling separatrix.

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English version:
Transactions of the Moscow Mathematical Society, 2018, 209–229

UDC: 517.925.41 + 514.763.81
MSC: 34C23, 34C37, 37J45
Received: 17.04.2018

Citation: A. V. Dukov, “Bifurcations of the ‘heart’ polycycle in generic 2-parameter families”, Tr. Mosk. Mat. Obs., 79, no. 2, MCCME, M., 2018, 247–269; Trans. Moscow Math. Soc., 2018, 209–229

Citation in format AMSBIB
\Bibitem{Duk18}
\by A.~V.~Dukov
\paper Bifurcations of the `heart' polycycle in generic 2-parameter families
\serial Tr. Mosk. Mat. Obs.
\yr 2018
\vol 79
\issue 2
\pages 247--269
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo615}
\elib{http://elibrary.ru/item.asp?id=37045100}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2018
\pages 209--229
\crossref{https://doi.org/10.1090/mosc/284}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85060869456}


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