Abstract
In this paper the perturbations of F4(x, y) = (y, −x2 + 4x) are considered. The existence of infinitely many critical homoclinic orbits for F4 makes this mapping a bifurcation point involving diverse dynamical structures. It is proved that there exist infinitely many codimension one submanifolds in the space of C2 endomorphisms, each of which accumulates on F4, is contained in the boundary of the set of hyperbolic mappings and is determined by the continuation of one of the homoclinic orbits of F4.
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