Three results on mixing shapes

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

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Abstract

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:	http://www.ams.org/mathscinet-getitem?mr... http://www.zentralblatt-math.org/zmath/e...
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:48
Last Modified:	15 Dec 2022 02:04
URI:	https://ueaeprints.uea.ac.uk/id/eprint/18608
DOI:

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