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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
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.
Received: 11.04.2014 Accepted: 25.04.2014
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
Linking options:
https://www.mathnet.ru/eng/rcd176 https://www.mathnet.ru/eng/rcd/v19/i4/p495
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Abstract page: | 170 | References: | 32 |
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