Miles, R. and Ward, T. (2006) 'Mixing actions of the rationals.', Ergodic theory and dynamical systems., 26 (6). pp. 1905-1911.
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.
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|Publisher Web site:||http://dx.doi.org/10.1017/S0143385706000356|
|Publisher 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|
|Record Created:||12 Oct 2012 11:50|
|Last Modified:||25 Oct 2012 12:06|
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