  We give a new proof of a theorem of Hubbard-Oberste-Vorth [HOV2] for H\'enon
maps that are perturbations of a hyperbolic polynomial and recover the Julia
set $J^{+}$ inside a polydisk as the image of the fixed point of a contracting
operator. We also give different characterizations of the Julia sets $J$ and
$J^{+}$ which prove useful for later applications.
