RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zhurnal SVMO:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zhurnal SVMO, 2016, Volume 18, Number 2, Pages 11–15 (Mi svmo588)  

Mathematics

Heteroclinic Curves of Gradient-like Diffeomorphsms and the Topology of Ambient Manifolds

V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka

State University – Higher School of Economics in Nizhnii Novgorod

Abstract: In the study of deterministic processes described by the Morse-Smale systems noncompact heteroclinic curves play special role. These curves belong to intersections of stable and unstable manifolds of saddle periodic points. In particular, these curves are mathematical models of magnetic separators in the plasma field. We consider the class of gradient-like diffeomorphisms on three-dimensional manifolds such that their periodic points and a part of their invariant manifolds form disjoint tamely embedded surfaces. We prove that the number of the surfaces is finite and all of them have the same genus. The main result is presentation of the exact lower estimation for the number of heteroclinic curves of any diffeomorphism from considered class. This estimation is defined by genus of surfaces and their number. In addition the paper describes the topological type of manifolds which admit considered diffeomorphisms.

Keywords: structurally stable dynamical systems, heteroclinic curves, mapping torus

Funding Agency Grant Number
HSE Basic Research Program 90
Russian Foundation for Basic Research 15-01-03687


Full text: PDF file (398 kB)
References: PDF file   HTML file
UDC: 517.938

Citation: V. Z. Grines, E. Ya. Gurevich, O. V. Pochinka, “Heteroclinic Curves of Gradient-like Diffeomorphsms and the Topology of Ambient Manifolds”, Zhurnal SVMO, 18:2 (2016), 11–15

Citation in format AMSBIB
\Bibitem{GriGurPoc16}
\by V.~Z.~Grines, E.~Ya.~Gurevich, O.~V.~Pochinka
\paper Heteroclinic Curves of Gradient-like Diffeomorphsms and the Topology of Ambient Manifolds
\jour Zhurnal SVMO
\yr 2016
\vol 18
\issue 2
\pages 11--15
\mathnet{http://mi.mathnet.ru/svmo588}
\elib{http://elibrary.ru/item.asp?id=26322686}


Linking options:
  • http://mi.mathnet.ru/eng/svmo588
  • http://mi.mathnet.ru/eng/svmo/v18/i2/p11

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
    Number of views:
    This page:25
    Full text:3
    References:7

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020