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Directional Kronecker algebra for $mathbb{Z}^q$-actions

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 نشر من قبل Chunlin Liu
 تاريخ النشر 2021
  مجال البحث
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In this paper, directional sequence entropy and directional Kronecker algebra for $mathbb{Z}^q$-systems are introduced. The relation between sequence entropy and directional sequence entropy are established. Meanwhile, direcitonal discrete spectrum systems and directional null systems are defined. It is shown that a $mathbb{Z}^q$-system has directional discrete spectrum if and only if it is directional null. Moreover, it turns out that a $mathbb{Z}^q$-system has directional discrete spectrum along $q$ linearly independent directions if and only if it has discrete spectrum.



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