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2013
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 Gonchenko S. V., Gonchenko V. S., Tatjer J. C. Bifurcations of Three-Dimensional Diffeomorphisms with Non-Simple Quadratic Homoclinic Tangencies and Generalized Hénon Maps 2007, vol. 12, no. 3, pp.  233-266 Abstract We study bifurcations of periodic orbits in two parameter general unfoldings of a certain type homoclinic tangency (called a generalized homoclinic tangency) to a saddle fixed point. We apply the rescaling technique to first return (Poincaré) maps and show that the rescaled maps can be brought to so-called generalized Hénon maps which have non-degenerate bifurcations of fixed points including those with multipliers $e^{\pm i \phi}$. On the basis of this, we prove the existence of infinite cascades of periodic sinks and periodic stable invariant circles. Keywords: homoclinic tangency, rescaling, generalized Henon map, bifurcation Citation: Gonchenko S. V., Gonchenko V. S., Tatjer J. C.,  Bifurcations of Three-Dimensional Diffeomorphisms with Non-Simple Quadratic Homoclinic Tangencies and Generalized Hénon Maps, Regular and Chaotic Dynamics, 2007, vol. 12, no. 3, pp. 233-266 DOI:10.1134/S156035470703001X