Renormalisable Henon-like Maps and Unbounded Geometry

We show that given a one parameter family $F_b$ of strongly dissipative infinitely renormalisable H'enon-like maps, parametrised by a quantity called the `average Jacobian’ $b$, the set of all parameters $b$ such that $F_b$ has a Cantor set with unbounded geometry has full Lebesgue measure.