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arXiv · 1412.0738

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
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Abstract

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.

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S. V. Gonchenko, I. I. Ovsyannikov, J. C. Tatjer. 2014-12-01. Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points. https://doi.org/10.1134/s1560354714040054

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