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CMFD, 2017, Volume 63, Issue 3, Pages 455–474 (Mi cmfd329)  

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

Dynamical systems and topology of magnetic fields in conducting medium

V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka

National Research University — Higher School of Economics, 25/12 Bolshaya Pecherskaya str., 603155 Nizhniy Novgorod, Russia

Abstract: We discuss application of contemporary methods of the theory of dynamical systems with regular and chaotic hyperbolic dynamics to investigation of topological structure of magnetic fields in conducting media. For substantial classes of magnetic fields, we consider well-known physical models allowing us to reduce investigation of such fields to study of vector fields and Morse–Smale diffeomorphisms as well as diffeomorphisms with nontrivial basic sets satisfying the $A$ axiom introduced by Smale. For the point-charge magnetic field model, we consider the problem of separator playing an important role in the reconnection processes and investigate relations between its singularities. We consider the class of magnetic fields in the solar corona and solve the problem of topological equivalency of fields in this class. We develop a topological modification of the Zeldovich funicular model of the nondissipative cinematic dynamo, constructing a hyperbolic diffeomorphism with chaotic dynamics that is conservative in the neighborhood of its transitive invariant set.

Funding Agency Grant Number
Russian Science Foundation 17-11-01041


DOI: https://doi.org/10.22363/2413-3639-2017-63-3-455-474

Full text: PDF file (312 kB)
References: PDF file   HTML file

UDC: 517.938

Citation: V. Z. Grines, E. V. Zhuzhoma, O. V. Pochinka, “Dynamical systems and topology of magnetic fields in conducting medium”, Differential and functional differential equations, CMFD, 63, no. 3, Peoples' Friendship University of Russia, M., 2017, 455–474

Citation in format AMSBIB
\Bibitem{GriZhuPoc17}
\by V.~Z.~Grines, E.~V.~Zhuzhoma, O.~V.~Pochinka
\paper Dynamical systems and topology of magnetic fields in conducting medium
\inbook Differential and functional differential equations
\serial CMFD
\yr 2017
\vol 63
\issue 3
\pages 455--474
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd329}
\crossref{https://doi.org/10.22363/2413-3639-2017-63-3-455-474}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Z. Grines, E. Ya. Gurevich, E. V. Zhuzhoma, O. V. Pochinka, “Classification of Morse–Smale systems and topological structure of the underlying manifolds”, Russian Math. Surveys, 74:1 (2019), 37–110  mathnet  crossref  crossref  adsnasa  isi  elib
  • Современная математика. Фундаментальные направления
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