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 forward and backward Julia sets. Secondly, we study the relation between any pair of skew products of Hénon maps in \(\mathbb C^3\) having the same (forward and backward) Julia sets. Also in the same spirit, we further establish a similar relation between skew products of Hénon maps fibered over a compact metric space, sharing the same Julia sets.

本文的目的是研究\（\ mathbb C ^ k \），\（k \ ge 3. \）中某些类别的自同构Julia集的刚性性质。首先，我们研究两个多项式移位之间的关系：就像\（\ mathbb C ^ k \），\（k \ ge 3 \）中的地图一样，它们共享相同的前向和后向Julia集。其次，我们研究具有相同（向前和向后）Julia集的\（\ mathbb C ^ 3 \）中的Hénon映射的任何一对斜积之间的关系。同样，本着同样的精神，我们还建立了在紧凑的度量空间上纤维化的Hénon映射的偏积之间的相似关系，它们共享相同的Julia集。