94-26 L. J. Diaz, J. Rocha, M. Viana

Saddle-node cycles and prevalence of strange attractors (88K, LaTeX) Jan 28, 94

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Abstract. We consider parametrized families of diffeomorphisms bifurcating through the creation of critical saddle-node cycles and we show that they exhibit H\'enon-like strange attractors for a set of parameter values which has positive Lebesgue density at the bifurcation value. This is the first example of a bifurcation mechanism displaying such prevalence of H\'enon-like chaotic behaviour. Furthermore, for open classes of these families the bifurcation parameter is also a point of positive density of hyperbolic dynamics.

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