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Mat. Sb., 1995, Volume 186, Number 3, Pages 3–18 (Mi msb18)  

This article is cited in 9 scientific papers (total in 9 papers)

Chaotic and strange attractors of a two-dimensional map

V. N. Belykh


Abstract: A family of continuous, invertible standard maps of the torus, cylinder and plane is considered in this paper. Sequences of bifurcations are studied which correspond to the transformation of an invariant curve to chaotic and strange attractors. The characteristic variations of complicated attractors are considered. Hyperbolicity conditions are obtained for the case of piecewise-smooth maps. The maps generating the Henon, Lozi, Belykh attractors belong to our class of standard maps.

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English version:
Sbornik: Mathematics, 1995, 186:3, 311–326

Bibliographic databases:

UDC: 514
MSC: 58F12, 58F13, 58F14
Received: 31.08.1994

Citation: V. N. Belykh, “Chaotic and strange attractors of a two-dimensional map”, Mat. Sb., 186:3 (1995), 3–18; Sb. Math., 186:3 (1995), 311–326

Citation in format AMSBIB
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\by V.~N.~Belykh
\paper Chaotic and strange attractors of a~two-dimensional map
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 3
\pages 3--18
\mathnet{http://mi.mathnet.ru/msb18}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1331805}
\zmath{https://zbmath.org/?q=an:0851.58033}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 3
\pages 311--326
\crossref{https://doi.org/10.1070/SM1995v186n03ABEH000018}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ92200001}


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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. Belykh V., Mosekilde E., “One-Dimensional Map Lattices: Synchronization, Bifurcations, and Chaotic Structures”, Phys. Rev. E, 54:4, Part a (1996), 3196–3203  crossref  mathscinet  adsnasa  isi
    2. Belykh V., “Homoclinic Orbits Bifurcations of One- and Two-Dimensional Maps”, Int. J. Bifurcation Chaos, 6:6 (1996), 1169–1176  crossref  mathscinet  zmath  isi
    3. Vladimir Belykh, Igor Belykh, Martin Hasler, “Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems”, Phys Rev E, 62:5 (2000), 6332  crossref  mathscinet  isi
    4. CHENG-HSIUNG HSU, “SMALE HORSESHOE OF CELLULAR NEURAL NETWORKS”, Int. J. Bifurcation Chaos, 10:09 (2000), 2119  crossref
    5. V.S Anishchenko, A.S Kopeikin, J Kurths, T.E Vadivasova, G.I Strelkova, “Studying hyperbolicity in chaotic systems”, Physics Letters A, 270:6 (2000), 301  crossref
    6. Cheng-Hsiung Hsu, Song-Sun Lin, “Spatial disorder of Cellular Neural Networks”, Japan J Indust Appl Math, 19:1 (2002), 143  crossref  mathscinet  zmath  isi
    7. V. S. Anishchenko, T. E. Vadivasova, G. A. Okrokvertskhov, G. I. Strelkova, “Statistical properties of dynamical chaos”, Phys. Usp., 48:2 (2005), 151–166  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    8. Antonio Pumariño, José Ángel Rodríguez, J.C.arles Tatjer, Enrique Vigil, “Chaotic dynamics for two-dimensional tent maps”, Nonlinearity, 28:2 (2015), 407  crossref
    9. Conchenko A.S., Conchenko V S., Kazakovt V O., Kozlov A.D., “Elements of Contemporary Theory of Dynamical Chaos: a Tutorial. Part i. Pseudohyperbolic Attractors”, Int. J. Bifurcation Chaos, 28:11 (2018), 1830036  crossref  mathscinet  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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