English

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

Dynamical Systems 2022-02-22 v4

Abstract

In this paper, directional sequence entropy and directional Kronecker algebra for Zq\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 Zq\mathbb{Z}^q-system has directional discrete spectrum if and only if it is directional null. Moreover, it turns out that a Zq\mathbb{Z}^q-system has directional discrete spectrum along qq linearly independent directions if and only if it has discrete spectrum.

Cite

@article{arxiv.2105.03130,
  title  = {Directional Kronecker algebra for $\mathbb{Z}^q$-actions},
  author = {Chunlin Liu and Leiye Xu},
  journal= {arXiv preprint arXiv:2105.03130},
  year   = {2022}
}
R2 v1 2026-06-24T01:52:09.924Z