Mixing and tight polyhedra

Ward, Thomas (2006) Mixing and tight polyhedra. IMS Lecture Notes - Monograph Series, 48. pp. 169-175.

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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.

Item Type: Article
Additional Information: in Dynamics & Stochastics: Festschrift in Honor of M. S. Keane (Dee Denteneer, Frank den Hollander and Evgeny Verbitskiy, Editors)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 16 Feb 2023 10:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/19719
DOI: 10.1214/074921706000000194

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