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Regul. Chaotic Dyn., 2014, Volume 19, Issue 4, Pages 495–505 (Mi rcd176)  

This article is cited in 8 scientific papers (total in 8 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

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)


DOI: https://doi.org/10.1134/S1560354714040054

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Bibliographic databases:

MSC: 37C05, 37G25, 37G35
Received: 11.04.2014
Accepted:25.04.2014
Language:

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://www.ams.org/mathscinet-getitem?mr=3240982}
\zmath{https://zbmath.org/?q=an:1335.37031}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000340380900005}


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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. A. S. Gonchenko, S. V. Gonchenko, “Variety of strange pseudohyperbolic attractors in three-dimensional generalized Hénon maps”, Physica D, 337 (2016), 43–57  crossref  mathscinet  zmath  isi  scopus
    2. Aminur Rahman, Yogesh Joshi, Denis Blackmore, “Sigma Map Dynamics and Bifurcations”, Regul. Chaotic Dyn., 22:6 (2017), 740–749  mathnet  crossref  mathscinet
    3. S. Gonchenko, I. Ovsyannikov, “Homoclinic tangencies to resonant saddles and discrete Lorenz attractors”, Discret. Contin. Dyn. Syst.-Ser. S, 10:2 (2017), 273–288  crossref  mathscinet  zmath  isi  scopus
    4. I. I. Ovsyannikov, V. D. Turaev, “Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model”, Nonlinearity, 30:1 (2017), 115–137  crossref  mathscinet  zmath  isi  scopus
    5. M. J. Capinski, D. Turaev, P. Zgliczynski, “Computer assisted proof of the existence of the Lorenz attractor in the Shimizu-Morioka system”, Nonlinearity, 31:12 (2018), 5410–5440  crossref  mathscinet  zmath  isi  scopus
    6. A. S. Conchenko, V S. Conchenko, V O. Kazakovt, A. D. Kozlov, “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
    7. J. Eilertsen, J. Magnan, “On the chaotic dynamics associated with the center manifold equations of double-diffusive convection near a codimension-four bifurcation point at moderate thermal Rayleigh number”, Int. J. Bifurcation Chaos, 28:8 (2018), 1850094  crossref  mathscinet  zmath  isi  scopus
    8. S. Gonchenko, M.-Ch. Li, M. Malkin, “Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders”, Dynam. Syst., 33:3 (2018), 441–463  crossref  mathscinet  zmath  isi  scopus
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