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

Abstract

We give a new proof of a theorem of Hubbard-Oberste-Vorth [HOV2] for Hénon 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.

15 pages, 3 figures

References in corpus (4)

• Henon mappings in the complex domain II: projective and inductive limits of polynomials
• A structure theorem for semi-parabolic Hénon maps
• Complex Hénon maps and discrete groups
• Semi-parabolic tools for hyperbolic Hénon maps and continuity of Julia sets in ${\mathbb{C}}^2$