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:: https://doi.org/10.1017/50143385706000356


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 - Does NOT include content added after October 2018: Faculty of Social Sciences and Humanities > Department of Teacher Education
Identification Number: https://doi.org/10.1017/50143385706000356
Page Range: 1905-1911
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 13:21
Last Modified: 18 Mar 2021 16:30
URI: https://shura.shu.ac.uk/id/eprint/17239

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