Mixing actions of the rationals

Miles, R.; Ward, T.

doi:10.1017/s0143385706000356

Mixing actions of the rationals

Miles, R.; Ward, T.

Authors

R. Miles

T. Ward

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

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Copyright Statement
© Copyright Cambridge University Press 2006.
This paper has been published in a revised form subsequent to editorial input by Cambridge University Press in "Ergodic theory and dynamical systems" (26: 6 (2006) 1905-1911) http://journals.cambridge.org/action/displayJournal?jid=ETS