Three results on mixing shapes

Ward, Tom (1997) Three results on mixing shapes. New York Journal of Mathematics, 3A. pp. 1-10.

[thumbnail of 3resmixingshapes.pdf]
PDF (3resmixingshapes.pdf) - Accepted Version
Download (247kB) | Preview


Let a be a Zd-action (d ³ 2) by automorphisms of a compact metric abelian group. For any non-linear shape I Ì Zd, there is an a with the property that I is a minimal mixing shape for a. The only implications of the form ``I is a mixing shape for a Þ J is a mixing shape for a'' are trivial ones for which I contains a translate of J. If all shapes are mixing for a, then a is mixing of all orders. In contrast to the algebraic case, if b is a Zd-action by measure-preserving transformations, then all shapes mixing for b does not preclude rigidity. Finally, we show that mixing of all orders in cones - a property that coincides with mixing of all orders for Z-actions - holds for algebraic mixing Z2-actions.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 15 Dec 2022 02:04


Downloads per month over past year

Actions (login required)

View Item View Item