VyacheslavZ. Grines, Elena Ya. Gurevich, Evgenii V. Zhuzhoma, Svetlana Kh. Zinina, “Heteroclinic curves of Morse–Smale cascades and separators in magnetic field of plasma”, Nelin. Dinam., 10:4 (2014), 427

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]

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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2014, Volume 10, Number 4, Pages 427–438 (Mi nd454)

This article is cited in 9 scientific papers (total in 9 papers)

Heteroclinic curves of Morse–Smale cascades and separators in magnetic field of plasma

VyacheslavZ. Grines^a, Elena Ya. Gurevich^b, Evgenii V. Zhuzhoma^b, Svetlana Kh. Zinina^c

^a N. I. Lobachevskii Nizhnii Novgorod State University, Gagarina pr. 23, Nizhnii Novgorod, 603950, Russia
^b National Research University Higher School of Economics, Bolshaya Pecherskaya 25/12, Nizhnii Novgorod, 603155, Russia
^c N. P. Ogarev State University of Mordovia, Bolshevistskaya 68, Saransk, 430005, Russia

Full-text PDF (394 kB) Citations (9)

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Abstract: We obtain properties of three-dimensional phase space and dynamics of Morse–Smale diffeomorphism that led to existence of at least one heteroclinical curve in non-wandering set of the diffeomorphism. We apply this result to solve a problem of existence of separators in magnetic field of plasma.

Keywords: Morse–Smale cascades, heteroclinic curves, mapping torus, locally trivial bundle, separators of magnetic field.

Received: 24.11.2014
Revised: 04.12.2014

Document Type: Article

UDC: 517.938, 514.83

MSC: 37E30

Language: Russian

Citation: VyacheslavZ. Grines, Elena Ya. Gurevich, Evgenii V. Zhuzhoma, Svetlana Kh. Zinina, “Heteroclinic curves of Morse–Smale cascades and separators in magnetic field of plasma”, Nelin. Dinam., 10:4 (2014), 427–438

Citation in format AMSBIB

\Bibitem{GriGurZhu14}

\by VyacheslavZ.~Grines, Elena~Ya.~Gurevich, Evgenii~V.~Zhuzhoma, Svetlana~Kh.~Zinina

\paper Heteroclinic curves of Morse--Smale cascades and separators in magnetic field of plasma

\jour Nelin. Dinam.

\yr 2014

\vol 10

\issue 4

\pages 427--438

\mathnet{http://mi.mathnet.ru/nd454}

Linking options:

https://www.mathnet.ru/eng/nd454

https://www.mathnet.ru/eng/nd/v10/i4/p427

This publication is cited in the following 9 articles:

Vyacheslav Z. Grines, Vladislav S. Medvedev, Evgeny V. Zhuzhoma, “On the Topological Structure of Manifolds Supporting Axiom A Systems”, Regul. Chaotic Dyn., 27:6 (2022), 613–628
Grines V.Z., Gurevich E.Ya., Kevlia S.S., “On Gradient-Like Flows on Seifert Manifolds”, Lobachevskii J. Math., 42:5, SI (2021), 901–910
V. Z. Grines, E. Ya. Gurevich, E. D. Kurenkov, “Topological Classification of Gradient-Like Flows with Surface Dynamics on $3$ -Manifolds”, Math. Notes, 107:1 (2020), 173–176
Vyacheslav Z. Grines, Elena Ya. Gurevich, Olga V. Pochinka, “On the Number of Heteroclinic Curves of Diffeomorphisms with Surface Dynamics”, Regul. Chaotic Dyn., 22:2 (2017), 122–135
E. V. Zhuzhoma, V. S. Medvedev, N. V. Isaenkova, “O topologicheskoi strukture magnitnogo polya oblastei fotosfery”, Nelineinaya dinam., 13:3 (2017), 399–412
V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka, “Dinamicheskie sistemy i topologiya magnitnykh polei v provodyaschei srede”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 63, no. 3, Rossiiskii universitet druzhby narodov, M., 2017, 455–474
A. N. Sakharov, A. A. Shilovskaya, “Potoki Morsa-Smeila i modeli topologii magnitnykh polei v plazme”, Zhurnal SVMO, 19:1 (2017), 88–101
M. L. Kolomiets, A. N. Sakharov, E. V. Tregubova, “O topologii potentsialnykh magnitnykh polei”, Zhurnal SVMO, 18:1 (2016), 31–44
V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “Geteroklinicheskie krivye gradientno-podobnykh diffeomorfizmov i topologiya nesuschego mnogoobraziya”, Zhurnal SVMO, 18:2 (2016), 11–15

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

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