Saddle-node Cycles and Prevalence of Strange Attractors

We consider parametrized families of diieomorphisms 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 rst 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 .