Geodesic
On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors
S.V. Gonchenko1 ; I.I. Ovsyannikov1, 2
1 Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str., 603005 Nizhny Novgorod, Russia
2 Imperial College, SW7 2AZ London, UK
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 71-83.

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We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransversal heteroclinic cycles. We show that bifurcations under consideration lead to the birth of Lorenz-like attractors. They can be viewed as attractors in the Poincare map for periodically perturbed classical Lorenz attractors and hence they can allow for the existence of homoclinic tangencies and wild hyperbolic sets.
DOI : 10.1051/mmnp/20138505

S.V. Gonchenko 1 ; I.I. Ovsyannikov 1, 2

1 Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str., 603005 Nizhny Novgorod, Russia
2 Imperial College, SW7 2AZ London, UK 
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S.V. Gonchenko; I.I. Ovsyannikov. On Global Bifurcations of Three-dimensional Diffeomorphisms Leading to Lorenz-like Attractors. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 71-83. doi : 10.1051/mmnp/20138505. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138505/

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