The purpose of this article is to study the relation between combinatorial equivalence and topological conjugacy, specifically how a certain type of combinatorial equivalence implies topological conjugacy. We introduce the concept of kneading sequences for a setting that is more general than one-dimensional dynamics: for the two-dimensional toy model family of Hénon maps introduced by Benedicks and Carleson, we define kneading sequences for their critical lines, and prove that these sequences are a complete invariant for a natural conjugacy class among the toy model family. We also establish a version of Singer’s theorem for the toy model family.

中文翻译：

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Hénon 地图玩具模型的揉捏序列

本文的目的是研究组合等价与拓扑共轭的关系，特别是某种组合等价如何蕴涵拓扑共轭。我们为比一维动力学更一般的设置引入了捏合序列的概念：对于 Benedicks 和 Carleson 引入的 Hénon 映射的二维玩具模型族，我们为其临界线定义了捏合序列，并证明这些序列是玩具模型家族中自然共轭类的完全不变量。我们还为玩具模型系列建立了 Singer 定理的一个版本。