Abstract
Let {fa,b} be the (original) Hénon family. In this paper, we show that, for any b near 0, there exists a closed interval Jb which contains a dense subset J′ such that, for any a ∊ J′, fa,b has a quadratic homoclinic tangency associated with a saddle fixed point of fa,b which unfolds generically with respect to the one-parameter family . By applying this result, we prove that Jb contains a residual subset such that, for any , fa,b admits the Newhouse phenomenon. Moreover, the interval Jb contains a dense subset such that, for any , fa,b has a large homoclinic set without SRB measure and a small strange attractor with SRB measure simultaneously.
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