A new proof of a theorem of Hubbard-Oberste-Vorth

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.