Rigidity of Julia sets of families of biholomorphic mappings in higher dimension

Abstract

The goal of this article is to study a rigidity property of Julia sets of certain classes of automorphisms in C k , k ≥ 3. First, we study the relation between two polynomial shift-like maps in C k , k ≥ 3, that share the same backward and forward Julia sets (or non-escaping sets). Secondly, we study the relation between any pair of skew products of Hénon maps in C 3 having the same forward and backward Julia sets.