论文标题
Todorcević的三分法和驯服动力系统类别的层次结构
Todorcević' trichotomy and a hierarchy in the class of tame dynamical systems
论文作者
论文摘要
Todorcević的三色切开术在可分离的Rosenthal Compacta等类别中引起了驯服（紧凑，Metrizable）动力学系统$（x，t）$的层次结构，并根据其包裹的Semigroups $ e（x）$的拓扑特性。更准确地说，我们定义类$ \ mathrm {tame} _ \ mathbf {2} \ subset \ subset \ mathrm {tame} _ \ mathbf {1} \ subset \ subset \ subset \ mathrm {tame}，$ \ syrm { $ e（x）$和$ \ mathrm {tame} _ \ mathbf {2} $是其适当的子类，由具有遗传性可分离$ e（x）$的系统组成。我们研究了这些类别的一些一般特性，并展示了许多例子来说明这些特性。
Todorcević' trichotomy in the class of separable Rosenthal compacta induces a hierarchy in the class of tame (compact, metrizable) dynamical systems $(X,T)$ according to the topological properties of their enveloping semigroups $E(X)$. More precisely, we define the classes $\mathrm{Tame}_\mathbf{2} \subset \mathrm{Tame}_\mathbf{1} \subset \mathrm{Tame},$ where $\mathrm{Tame}_\mathbf{1}$ is the proper subclass of tame systems with first countable $E(X)$, and $\mathrm{Tame}_\mathbf{2}$ is its proper subclass consisting of systems with hereditarily separable $E(X)$. We study some general properties of these classes and exhibit many examples to illustrate these properties.
