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We consider dynamical systems, consisting of
-actions by continuous automorphisms on shift-invariant subgroups of
is the field of order
. These systems provide natural generalizations of Ledrappier’s system, which was the first example of a 2-mixing
-action that is not 3-mixing. Extending the results from our previous work on Ledrappier’s example, we show that, under quite mild conditions (namely, 2-mixing and that the subgroup defining the system is a principal Markov subgroup), these systems are almost strongly mixing of every order in the following sense: for each order, one just needs to avoid certain effectively computable logarithmically small sets of times at which there is a substantial deviation from mixing of this order.
We consider Ledrappier’s dynamical system, which was the first example of a -action which is 2-mixing but not 3-mixing. Our main result is that, excluding certain small ‘constructible’ sets, the system is mixing of every order.
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