混合和紧多面体
Mixing and tight polyhedra
摘要：
紧零维群的自同构对$\mathbb{Z}^d$的作用表现出一系列的混合行为。施密特为这些系统引入了混合形状的概念，并证明了非混合形状只能在零维群上的作用中出现。Masser已经表明，高阶混合的失败总是由非混合形状见证的。在这里，我们将展示如何使用估值来理解某个例子族的（非）混合行为。最清晰的信息出现在对应于紧密多面体的系统中。
英文摘要：
Actions of $\mathbb{Z}^d$ by automorphisms of compact zero-dimensional groups exhibit a range of mixing behaviour. Schmidt introduced the notion of mixing shapes for these systems, and proved that non-mixing shapes can only arise non-trivially for actions on zero-dimensional groups. Masser has shown that the failure of higher-order mixing is always witnessed by non-mixing shapes. Here we show how valuations can be used to understand the (non-)mixing behaviour of a certain family of examples. The sharpest information arises for systems corresponding to tight polyhedra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
