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VOL. 48 | 2006 Mixing and tight polyhedra
Thomas Ward

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 169-175 (2006) DOI: 10.1214/074921706000000194

## Abstract

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.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1167.37304
MathSciNet: MR2306198

Digital Object Identifier: 10.1214/074921706000000194

Subjects:
Primary: 22D40
Secondary: 52B11

Keywords: Mixing , polyhedra