论文标题
拓扑动力学和厄贡理论的远端系统
Distal systems in topological dynamics and ergodic theory
论文作者
论文摘要
我们将Lindenstrauss的结果推广到可测量和拓扑动力学之间的相互作用上，这表明每个可分开的沿距离可分离的可测量远端动力学系统都具有最小的远端模型。我们表明，实际上可以完全选择这样的模型。该结构是通过穿过远端系统的furstenberg-Zimmer塔来执行的，并表明在每个步骤中，都有一个简单且规范的远端最小模型。这取决于拓扑动力学中等距扩展的新表征。
We generalize a result of Lindenstrauss on the interplay between measurable and topological dynamics which shows that every separable ergodic measurably distal dynamical system has a minimal distal model. We show that such a model can, in fact, be chosen completely canonically. The construction is performed by going through the Furstenberg--Zimmer tower of a measurably distal system and showing that at each step, there is a simple and canonical distal minimal model. This hinges on a new characterization of isometric extensions in topological dynamics.
