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arXiv · 1903.01760

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

Sayani Bera·Ratna Pal
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Abstract

The goal of this article is to study a rigidity property of Julia sets of certain classes of automorphisms in $\mathbb{C}^k$, $k \ge 3.$ First, we study the relation between two polynomial shift-like maps in $\mathbb{C}^k$, $k \ge 3$, 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 H\'{e}non maps in $\mathbb{C}^3$ having the same forward and backward Julia sets.

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Sayani Bera, Ratna Pal. 2019-03-05. Rigidity of Julia sets of families of biholomorphic mappings in higher dimension. https://arxiv.org/abs/1903.01760

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