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JOURNALS // Russian Journal of Nonlinear Dynamics // Archive

Nelin. Dinam., 2010 Volume 6, Number 1, Pages 61–77 (Mi nd56)

This article is cited in 5 papers

On bifurcations of three-dimensional diffeomorphisms with a non-transversal heteroclinic cycle containing saddle-foci

S. V. Gonchenko, I. I. Ovsyannikov

Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod

Abstract: We study bifurcations of of three-dimensional diffeomorphisms with non-transversal heteroclinic cycles which lead to the birth of wild hyperbolic Lorenz-like attractors. As known, such attractors can be appeared under small periodic perturbations of the classical Lorenz attractor and they allow homoclinic tangencies, however, do not contain stable periodic orbits.

Keywords: homoclinic and heteroclinic orbit, bifurcation, strange attractor, saddle-focus.

UDC: 517.9

MSC: 37C05, 37C29, 37G25, 37G35

Received: 23.11.2009



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