Mixing and tight polyhedra

Thomas Ward

Research output: Contribution to journalArticlepeer-review


Actions of Zd 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.
Original languageEnglish
Pages (from-to)169-175
Number of pages7
JournalIMS Lecture Notes - Monograph Series
Publication statusPublished - 2006

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