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Nelin. Dinam., 2010, Volume 6, Number 1, Pages 61–77 (Mi nd56)  

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

On bifurcations of three-dimensional diffeomorphisms with a non-transversal heteroclinic cycle containing saddle-foci

S. V. Gonchenko, I. I. Ovsyannikov

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: We study bifurcations of of three-dimensional diffeomorphisms with non-transversal heteroclinic cycles which lead to the birth of wild hyperbolic Lorenz-like attractors. As known, such attractors can be appeared under small periodic perturbations of the classical Lorenz attractor and they allow homoclinic tangencies, however, do not contain stable periodic orbits.

Keywords: homoclinic and heteroclinic orbit, bifurcation, strange attractor, saddle-focus.

Full text: PDF file (1262 kB)
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UDC: 517.9
MSC: 37C05, 37C29, 37G25, 37G35
Received: 23.11.2009

Citation: S. V. Gonchenko, I. I. Ovsyannikov, “On bifurcations of three-dimensional diffeomorphisms with a non-transversal heteroclinic cycle containing saddle-foci”, Nelin. Dinam., 6:1 (2010), 61–77

Citation in format AMSBIB
\Bibitem{GonOvs10}
\by S.~V.~Gonchenko, I.~I.~Ovsyannikov
\paper On bifurcations of three-dimensional diffeomorphisms with a non-transversal heteroclinic cycle containing saddle-foci
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 1
\pages 61--77
\mathnet{http://mi.mathnet.ru/nd56}
\elib{http://elibrary.ru/item.asp?id=13411468}


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    This publication is cited in the following articles:
    1. Gonchenko S.V., Ovsyannikov I.I., Tatjer J.C., “Birth of Discrete Lorenz Attractors At the Bifurcations of 3D Maps With Homoclinic Tangencies to Saddle Points”, Regul. Chaotic Dyn., 19:4 (2014), 495–505  crossref  isi
    2. S. V. Gonchenko, D. V. Turaev, “On three types of dynamics and the notion of attractor”, Proc. Steklov Inst. Math., 297 (2017), 116–137  mathnet  crossref  crossref  mathscinet  isi  elib
  • Нелинейная динамика
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