Two-parameter areal scaling in the Hénon map

We study a bifurcation cascade whose proper unfolding requires tuning more than one parameter simultaneously. Specifically, we investigate metric properties of extended self-similar triangular areas observed recently in the control parameter space of flows (lasers and electronic circuits), and maps. Such areas are delimited by shrimplike stability islands, seem to arise in unbounded quantities, and to accumulate in narrow intervals of control parameters. Numerically, we find their asymptotic rate of accumulation to be unity. The asymptotic properties of triangle vertices and their centroids are also investigated.