Mixing actions of the rationals

Miles, R.; Ward, T.

Abstract

We study mixing properties of algebraic actions of Q^d, showing in particular that prime mixing Q^d-actions on connected groups are mixing of all orders, as is the case for 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 Q* are shown to behave quite differently, with finite order of mixing possible on connected groups.

Citation

Miles, R., & Ward, T. (2006). Mixing actions of the rationals. Ergodic Theory and Dynamical Systems, 26(6), 1905-1911. https://doi.org/10.1017/s0143385706000356

• Journal Article Type: Article
• Publication Date: Dec 1, 2006
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Oct 24, 2012
• Journal: Ergodic Theory and Dynamical Systems
• Print ISSN: 0143-3857
• Electronic ISSN: 1469-4417
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 6
• Pages: 1905-1911
• DOI: https://doi.org/10.1017/s0143385706000356
• Public URL: https://durham-repository.worktribe.com/output/1472280