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arXiv:1412.0738 [math.DS]AbstractReferencesReviewsResources

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

S. V. Gonchenko. I. I. Ovsyannikov, J. C. Tatjer

Published 2014-12-01Version 1

It was established in 2006 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 non-simple.

Journal: Regular and Chaotic Dynamics, 2014, Vol. 19, No. 4, pp. 495-505
Categories: math.DS
Subjects: 37C05, 37G25, 37G35
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