On global bifurcations in three-dimensional diffeomorphisms leading to wild Lorenz-like attractors

We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors,...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2009-02, Vol.14 (1), p.137-147
Main Authors: Gonchenko, S. V., Shilnikov, L. P., Turaev, D. V.
Format: Article
Language:English
Subjects:
Dynamical Systems and Ergodic Theory
Jürgen Moser-80
Mathematics
Mathematics and Statistics
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Summary:We study dynamics and bifurcations of three-dimensional diffeomorphisms with nontransverse heteroclinic cycles. We show that bifurcations under consideration lead to the birth of wild-hyperbolic Lorenz attractors. These attractors can be viewed as periodically perturbed classical Lorenz attractors, however, they allow for the existence of homoclinic tangencies and, hence, wild hyperbolic sets.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354709010092