Mixing actions of the rationals

MILES, Richard and WARD, Thomas (2006). Mixing actions of the rationals. Ergodic Theory and Dynamical Systems, 26 (6), 1905-1911.

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Official URL: https://doi.org/10.1017/50143385706000356
Link to published version:: 10.1017/50143385706000356

Abstract

We study mixing properties of algebraic actions of $\mathbb Q^d$, showing in particular that prime mixing $\mathbb Q^d$ actions on connected groups are mixing of all orders, as is the case for $\mathbb Z^d$-actions. This is shown using a uniform result on the solution of $S$-unit equations in characteristic zero fields due to Evertse, Schlickewei and W. Schmidt. In contrast, algebraic actions of the much larger group $\mathbb Q^*$ are shown to behave quite differently, with finite order of mixing possible on connected groups.

Item Type: Article
Departments: Development and Society > Teacher Education
Identification Number: 10.1017/50143385706000356
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 13:21
Last Modified: 26 Jan 2018 13:21
URI: http://shura.shu.ac.uk/id/eprint/17239

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