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

2019/03/05 by Bera, Sayani, Pal, Ratna
#32F45 #32Q45 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.01760

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 relationship between any pair of skew products of Hénon maps in ℂ³ having the same forward and backward Julia sets.

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