论文标题
狂野的行动
Wild Cantor actions
论文作者
论文摘要
$ g $在cantor套装$ x $上的最低限度等均匀行动的判别组是$ x $的同构同构中的诉讼的子组，包括固定给定点的同构态度。与该动作相关的稳定器和中心体组作为具有某些特性的判别组亚组序列的直接限制。 Cantor上的最小均值群体动作允许稳定器和Centralizer Direct Limit组的性质进行分类。 在本文中，我们在Cantor集合中构建了最小的等效行动的新家族，这说明了此分类的某些方面。这些示例被构造为在根树上的作用。表演组是产品的可数亚组或组的花环产物。我们讨论了我们的结果应用于动力学系统吸引子和最小叶子集的吸引者的应用。
The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and the centralizer groups associated to the action are obtained as direct limits of sequences of subgroups of the discriminant group with certain properties. Minimal equicontinuous group actions on Cantor sets admit a classification by the properties of the stabilizer and centralizer direct limit groups. In this paper, we construct new families of examples of minimal equicontinuous actions on Cantor sets, which illustrate certain aspects of this classification. These examples are constructed as actions on rooted trees. The acting groups are countable subgroups of the product or of the wreath product of groups. We discuss applications of our results to the study of attractors of dynamical systems and of minimal sets of foliations.
