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Regul. Chaotic Dyn., 2017, Volume 22, Issue 2, Pages 122–135 (Mi rcd246)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Number of Heteroclinic Curves of Diffeomorphisms with Surface Dynamics

Vyacheslav Z. Grines, Elena Ya. Gurevich, Olga V. Pochinka

National Research University Higher School of Economics, ul. Bolshaya Pecherskaya 25/12, Nizhny Novgorod, 603155 Russia

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

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03687-a
16-51-10005-Ko_a
Russian Science Foundation 14-41-00044
Ministry of Education and Science of the Russian Federation 90
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.


DOI: https://doi.org/10.1134/S1560354717020022

References: PDF file   HTML file

Bibliographic databases:

MSC: 37D20, 37D15
Received: 10.10.2016
Accepted:17.11.2016
Language:

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

Citation in format AMSBIB
\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
\mathnet{http://mi.mathnet.ru/rcd246}
\crossref{https://doi.org/10.1134/S1560354717020022}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000398060800002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016992106}


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

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  elib
    2. 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  mathnet  crossref  crossref  isi
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