We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems, a class that includes systems in which all orbit closures are minimal, have isomorphic K-theory if and only if the dynamical systems are strong orbit equivalent. Under the additional assumption that the dynamical systems have no periodic points, this gives a classification theorem including isomorphism of the associated crossed product $C^*$ -algebras as well. We additionally explore the K-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems.

中文翻译：

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纤维本质最小零维动力系统交叉积的动力分类


我们证明，纤维本质上最小的零维动力系统（一类包括所有轨道闭包都最小的系统）的交叉积，当且仅当动力系统是强轨道等效时才具有同构 K 理论。在动力系统没有周期点的附加假设下，这给出了一个分类定理，包括相关交叉积 $C^*$ -代数的同构。我们还探讨了此类交叉产品的 K 理论以及与动力系统相关的 Bratteli 图。