Beschreibung:
<jats:p>We consider dynamical systems, consisting of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385717000608_inline1" /><jats:tex-math>$\mathbb{Z}^{2}$</jats:tex-math></jats:alternatives></jats:inline-formula>-actions by continuous automorphisms on shift-invariant subgroups of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385717000608_inline2" /><jats:tex-math>$\mathbb{F}_{p}^{\mathbb{Z}^{2}}$</jats:tex-math></jats:alternatives></jats:inline-formula>, where <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385717000608_inline3" /><jats:tex-math>$\mathbb{F}_{p}$</jats:tex-math></jats:alternatives></jats:inline-formula> is the field of order <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385717000608_inline4" /><jats:tex-math>$p$</jats:tex-math></jats:alternatives></jats:inline-formula>. These systems provide natural generalizations of Ledrappier’s system, which was the first example of a 2-mixing <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385717000608_inline5" /><jats:tex-math>$\mathbb{Z}^{2}$</jats:tex-math></jats:alternatives></jats:inline-formula>-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.</jats:p>