Open AccessDynamical Systems and Topology of Magnetic Fields in Conducting Medium
Author(s) -
V. Z. Grines,
Вячеслав Зигмундович Гринес,
Е. В. Жужома,
Е. В. Жужома,
O. V. Pochinka,
O. V. Pochinka
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-3-455-474
Subject(s) - gravitational singularity , topology (electrical circuits) , topological quantum number , physics , invariant (physics) , topological dynamics , topological entropy , dynamical systems theory , chaotic , mathematics , pure mathematics , theoretical physics , computer science , mathematical analysis , mathematical physics , biochemistry , chemistry , topological tensor product , quantum mechanics , combinatorics , functional analysis , artificial intelligence , gene
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 elds in conducting media. For substantial classes of magnetic elds, we consider well-known physical models allowing us to reduce investigation of such elds to study of vector elds and Morse-Smale dieomorphisms as well as dieomorphisms with nontrivial basic sets satisfying the A axiom introduced by Smale. For the point-charge magnetic eld 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 elds in the solar corona and solve the problem of topological equivalency of elds in this class. We develop a topological modication of the Zeldovich funicular model of the nondissipative cinematic dynamo, constructing a hyperbolic dieomorphism with chaotic dynamics that is conservative in the neighborhood of its transitive invariant set.