, Volume 125, Issue 1, pp 37-74

Strange attractors in saddle-node cycles: prevalence and globality

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Abstract

 We consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle-node cycles. We show that they always exhibit Hénon-like strange attractors for a set of parameter values with positive Lebesgue density at the bifurcation value. In open classes of such families the strange attractors are of global type: their basins contain an a priori defined neighbourhood of the cycle. Furthermore, the bifurcation parameter may also be a point of positive density of hyperbolic dynamics.

Oblatum VIII-1993 & 23-II-1995