Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points

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 w...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2014-07, Vol.19 (4), p.495-505
Main Authors: Gonchenko, Sergey V., Ovsyannikov, Ivan I., Tatjer, Joan C.
Format: Article
Language:English
Subjects:
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354714040054