Birth of Discrete Lorenz Attractors at the Bifurcations of 3D Maps with Homoclinic Tangencies to Saddle Points

    2014, Volume 19, Number 4, pp.  495-505

    Author(s): Gonchenko S. V., Ovsyannikov I. I., Tatjer J. C.

    It was established in [1] 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 nonsimple.
    Keywords: Homoclinic tangency, rescaling, 3D Hénon map, bifurcation, Lorenz-like attractor
    Citation: Gonchenko S. V., Ovsyannikov I. I., Tatjer J. C., Birth of Discrete Lorenz Attractors at the Bifurcations of 3D Maps with Homoclinic Tangencies to Saddle Points, Regular and Chaotic Dynamics, 2014, Volume 19, Number 4, pp. 495-505



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