## Institute for Mathematical Sciences

## Preprint ims97-11

** J. Hubbard, P. Papadopol, and V. Veselov**
* A Compactification of Henon Mappings in $C^2$ as Dynamical Systems*

Abstract: 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.

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