Regular and Chaotic Dynamics

, Volume 22, Issue 2, pp 122–135 | Cite as

On the number of heteroclinic curves of diffeomorphisms with surface dynamics

  • Vyacheslav Z. GrinesEmail author
  • Elena Ya. Gurevich
  • Olga V. Pochinka


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.


separator in a magnetic field heteroclinic curves mapping torus gradient-like diffeomorphisms 

MSC2010 numbers

37D20 37D15 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • Vyacheslav Z. Grines
    • 1
    Email author
  • Elena Ya. Gurevich
    • 1
  • Olga V. Pochinka
    • 1
  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia

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