Abstract:
Separators are fundamental plasma physics objects that play an important role in many astrophysical phenomena. Looking for separators and their number is one of the first steps in studying the topology of the magnetic field in the solar corona. In the language of dynamical systems, separators are noncompact heteroclinic curves. In this paper we give an exact lower estimation of the number of noncompact heteroclinic curves for a 3-diffeomorphism with the so-called “surface dynamics”. Also, we prove that ambient manifolds for such diffeomorphisms are mapping tori.
Keywords:
separator in a magnetic field, heteroclinic curves, mapping torus, gradient-like diffeomorphisms.
The publication was supported by the Russian Foundation for Basic Research (project No. 15-01-03687-a, 16-51-10005-Ko a), Russian Science Foundation (project No. 14-41-00044) and the Basic Research Program at the HSE (project 90) in 2017.
Citation:
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
\Bibitem{GriGurPoc17}
\by Vyacheslav Z. Grines, Elena Ya. Gurevich, Olga V. Pochinka
\paper On the Number of Heteroclinic Curves of Diffeomorphisms with Surface Dynamics
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 2
\pages 122--135
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\crossref{https://doi.org/10.1134/S1560354717020022}
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Linking options:
https://www.mathnet.ru/eng/rcd246
https://www.mathnet.ru/eng/rcd/v22/i2/p122
This publication is cited in the following 7 articles:
E. I. Yakovlev, “Teorema suschestvovaniya dlya nakrytii rassloenii Serra”, Izv. vuzov. Matem., 2023, no. 3, 90–1
E. I. Yakovlev, “Existence Theorem for Coverings of Serre Bundles”, Russ Math., 67:3 (2023), 76
V. Z. Grines, O. V. Pochinka, E. E. Chilina, “Dynamics of 3-Homeomorphisms with Two-Dimensional Attractors and Repellers”, J Math Sci, 270:5 (2023), 683
V. Z. Grines, E. Ya. Gurevich, E. I. Yakovlev, “O topologii mnogoobrazii, dopuskayuschikh gradientno-podobnye kaskady s poverkhnostnoi dinamikoi, i roste chisla nekompaktnykh geteroklinicheskikh krivykh”, Zhurnal SVMO, 23:4 (2021), 379–393
V. Z. Grines, E. Ya. Gurevich, S. S. Kevlia, “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
E. Ya. Gurevich, D. A. Pavlova, “O prosteishikh potokakh Morsa-Smeila s geteroklinicheskimi peresecheniyami na sfere $S^n$”, Zhurnal SVMO, 19:2 (2017), 25–30
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