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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2017, Volume 19, Number 2, Pages 25–30
DOI: https://doi.org/10.15507/2079-6900.19.201701.025-030
(Mi svmo657)
 

This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On the simplest Morse-Smale flows with heteroclinical intersections on the sphere $S^n$

E. Ya. Gurevich, D. A. pavlova

National Research University – Higher School of Economics in Nizhny Novgorod
Full-text PDF (442 kB) Citations (1)
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Abstract: This paper is the first step in stydying structure of decomposition of phase space with dimension $n\geq 4$ on the trajectories of Morse-Smale flows (structurally stable flows with non-wandering set consisting of finite number of equilibria and closed trajectories) allowing heteroclinic intersections. More precisely, special class of Morse-Smale flows on the sphere $S^n$ is studied. The non-wandering set of the flow of interest consists of two nodal and two saddle equilibrium states. It is proved that for every flow from the class under consideration the intersection of invariant manifolds of two different saddle equilibrium states is nonempty and consists of a finite number of connectivity components. Heteroclinic intersections are mathematical models for magnetic field separators. Study of their structure, as well as the question of their existence, is one of the principal problems of magnetic hydrodynamics.
Keywords: Morse-Smale flows, heteroclinic intersections.
Funding agency Grant number
HSE Basic Research Program 90
Russian Foundation for Basic Research 15-01-03687
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 37D15
Language: Russian
Citation: E. Ya. Gurevich, D. A. pavlova, “On the simplest Morse-Smale flows with heteroclinical intersections on the sphere $S^n$”, Zhurnal SVMO, 19:2 (2017), 25–30
Citation in format AMSBIB
\Bibitem{GurPav17}
\by E.~Ya.~Gurevich, D.~A.~pavlova
\paper On the simplest Morse-Smale flows with heteroclinical intersections on the sphere $S^n$
\jour Zhurnal SVMO
\yr 2017
\vol 19
\issue 2
\pages 25--30
\mathnet{http://mi.mathnet.ru/svmo657}
\crossref{https://doi.org/10.15507/2079-6900.19.201701.025-030}
\elib{https://elibrary.ru/item.asp?id=29783059}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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