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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 4, Pages 495–505
DOI: https://doi.org/10.1134/S1560354714040054 (Mi rcd176) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Birth of Discrete Lorenz Attractors at the Bifurcations of 3D Maps with Homoclinic Tangencies to Saddle Points

Sergey V. Gonchenkoa, Ivan I. Ovsyannikovab, Joan C. Tatjerc

a Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603000 Russia
b Imperial College London, SW7 2AZ, London, UK
c Dept. de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
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DOI: https://doi.org/10.1134/S1560354714040054
Abstract: It was established in [1] that bifurcations of three-dimensional diffeomorphisms with a homoclinic tangency to a saddle-focus fixed point with the Jacobian equal to 1 can lead to Lorenz-like strange attractors. In the present paper we prove an analogous result for three-dimensional diffeomorphisms with a homoclinic tangency to a saddle fixed point with the Jacobian equal to 1, provided the quadratic homoclinic tangency under consideration is nonsimple.
Keywords: Homoclinic tangency, rescaling, 3D Hénon map, bifurcation, Lorenz-like attractor.
Funding agency Grant number
Russian Science Foundation 14-12-00811
Russian Foundation for Basic Research 13-01-00589
13-01-97028-povolzhje
14-01-00344
Ministry of Education and Science of the Russian Federation 02.B.49.21.0003
Leverhulme Trust RPG-279
Engineering and Physical Sciences Research Council EP/I019111/1
Ministerio de Educación y Ciencia, Spain MTM2009-09723
Section 3 is carried out by the RSF-grant (project No. 14-12-00811). The paper was partially supported by the grants of RFBR No. 13-01-00589, 13-01-97028–povolzhje and 14-01-00344. The first author was supported by the grant (the agreement of August 27, 2013 No. 02.B.49.21.0003 between The Ministry of education and science of the Russian Federation and Lobachevsky State University of Nizhni Novgorod). The second author was supported by the Leverhulme Trust grant RPG-279 and the EPSRC Mathematics Platform grant EP/I019111/1. The third author was supported by the MEC grant MTM2009-09723 (Spain) and the CIRIT grant 2009 SGR 67 (Spain)
Received: 11.04.2014
Accepted: 25.04.2014
Bibliographic databases:
Document Type: Article
MSC: 37C05, 37G25, 37G35
Language: English
Citation: Sergey V. Gonchenko, Ivan I. Ovsyannikov, Joan C. Tatjer, “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
Citation in format AMSBIB
\Bibitem{GonOvsTat14}
\by Sergey~V.~Gonchenko, Ivan~I.~Ovsyannikov, Joan~C.~Tatjer
\paper Birth of Discrete Lorenz Attractors at the Bifurcations of 3D Maps with Homoclinic Tangencies to Saddle Points
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 4
\pages 495--505
\mathnet{http://mi.mathnet.ru/rcd176}
\crossref{https://doi.org/10.1134/S1560354714040054}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3240982}
\zmath{https://zbmath.org/?q=an:1335.37031}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340380900005}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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