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  • Ergodic Theory and Dynamical Systems, Volume 26, Issue 6
  • December 2006, pp. 1905-1911

Mixing actions of the rationals

  • RICHARD MILES (a1) and TOM WARD (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385706000356
  • Published online: 07 September 2006
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.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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