A rigidity theorem for Hénon maps

Abstract

The purpose of this note is two fold. First, we study the relation between a pair of Hénon maps that share the same forward and backward non-escaping sets. Second, it is shown that there exists a continuum of $Short-{\mathbb{C}}^2$'s that are biholomorphically inequivalent and finally, we provide examples of $Short-{\mathbb{C}}^2$'s that are neither Reinhardt nor biholomorphic to Reinhardt domains.

19 pages