Mixing actions of the rationals

Details Mixing actions of the rationals Mixing actions of the rationals

2005-01-10

arxiv.org/abs/math/0501142v1

Ergodic Theory and Dynamical Systems, 26, No. 6, 1905-1911 (2006)

Mathematics

Dynamical Systems

Scientific paper

10.1017/S0143385706000356

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 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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