  In \cite {HO1}, it was shown that there is a topology on $\C^2\sqcup S^3$
homeomorphic to a 4-ball such that the H\'enon mapping extends continuously.
That paper used a delicate analysis of some asymptotic expansions, for
instance, to understand the structure of forward images of lines near infinity.
The computations were quite difficult, and it is not clear how to generalize
them to other rational maps.
  In this paper we will present an alternative approach, involving blow-ups
rather than asymptotics. We apply it here only to H\'enon mappings and their
compositions, but the method should work quite generally, and help to
understand the dynamics of rational maps $f:\Proj^2\ratto\Proj^2$ with points
of indeterminacy. The application to compositions of H\'enon maps proves a
result suggested by Milnor, involving embeddings of solenoids in $S^3$ which
are topologically different from those obtained from H\'enon mappings.
