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 -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 -system has directional discrete spectrum if and only if it is directional null. Moreover, it turns out that a -system has directional discrete spectrum along 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}
}