RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Uspekhi Mat. Nauk, 2002, Volume 57, Issue 6(348), Pages 123–166 (Mi umn574)  

This article is cited in 6 scientific papers (total in 7 papers)

On the problem of topological classification of strange attractors of dynamical systems

R. V. Plykin

Obninsk State Technical University for Nuclear Power Engineering

Abstract: This paper consists of two parts. The first, which is devoted to presenting results of Barge and Watkins, connects the closure of the union of the unstable manifolds of certain “Smale horseshoes” with Knaster continua and projections on them of Vietoris–van Dantzig solenoids. In the second part the homeomorphism problem for expanding attractors of codimension 1 is solved when the dimension of the manifold generating the dynamical system is greater than two.

DOI: https://doi.org/10.4213/rm574

Full text: PDF file (564 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2002, 57:6, 1163–1205

Bibliographic databases:

UDC: 517.938.5+515.16
MSC: Primary 37D45; Secondary 37D20, 37C85, 37D15, 57R30
Received: 17.10.2000

Citation: R. V. Plykin, “On the problem of topological classification of strange attractors of dynamical systems”, Uspekhi Mat. Nauk, 57:6(348) (2002), 123–166; Russian Math. Surveys, 57:6 (2002), 1163–1205

Citation in format AMSBIB
\Bibitem{Ply02}
\by R.~V.~Plykin
\paper On the problem of topological classification of strange attractors of dynamical systems
\jour Uspekhi Mat. Nauk
\yr 2002
\vol 57
\issue 6(348)
\pages 123--166
\mathnet{http://mi.mathnet.ru/umn574}
\crossref{https://doi.org/10.4213/rm574}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1991864}
\zmath{https://zbmath.org/?q=an:1046.37017}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2002RuMaS..57.1163P}
\elib{http://elibrary.ru/item.asp?id=14240300}
\transl
\jour Russian Math. Surveys
\yr 2002
\vol 57
\issue 6
\pages 1163--1205
\crossref{https://doi.org/10.1070/RM2002v057n06ABEH000574}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182349100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0038326678}


Linking options:
  • http://mi.mathnet.ru/eng/umn574
  • https://doi.org/10.4213/rm574
  • http://mi.mathnet.ru/eng/umn/v57/i6/p123

    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

    This publication is cited in the following articles:
    1. R. V. Plykin, “Strange attractors of $A$-cascades”, Russian Math. Surveys, 59:2 (2004), 390–392  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Zhirov, “Combinatorics of One-Dimensional Hyperbolic Attractors of Diffeomorphisms of Surfaces”, Proc. Steklov Inst. Math., 244 (2004), 132–200  mathnet  mathscinet  zmath
    3. Grines V.Z., Zhuzhoma E.V., “Expanding attractors”, Regul. Chaotic Dyn., 11:2 (2006), 225–246  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. Elhadj Z., Sprott J.C., “On the robustness of chaos in dynamical systems: Theories and applications”, Front Phys China, 3:2 (2008), 195–204  crossref  adsnasa  isi  elib  scopus  scopus
    5. Plykin R.V., Klinshpont N.E., “Strange attractors. Topologic, geometric and algebraic aspects”, Regular & Chaotic Dynamics, 15:2–3 (2010), 335–347  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. D. V. Anosov, M. Ya. Antonovskii, V. M. Buchstaber, V. Z. Grines, A. Yu. Zhirov, E. V. Zhuzhoma, N. È. Klinshpont, A. A. Mal'tsev, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, L. P. Shil'nikov, “Romen Vasil'evich Plykin (obituary)”, Russian Math. Surveys, 66:3 (2011), 627–631  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. A. Yu. Zhirov, “How Many Different Cascades on a Surface Can Have Coinciding Hyperbolic Attractors?”, Math. Notes, 94:1 (2013), 96–106  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:504
    Full text:183
    References:37
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019