A Study of Directional Entropy Arising from $\mathbb{Z} \times \mathbb{Z}_+$ Semigroup Actions

Hasan Akin

A Study of Directional Entropy Arising from $\mathbb{Z} \times \mathbb{Z}_+$ Semigroup Actions

Dynamical Systems 2025-05-16 v1

Authors: Hasan Akin

Abstract

In this chapter, we investigate directional entropy for semigroup actions generated by one-dimensional linear cellular automata (LCAs) and the shift transformation on the compact metric space $\mathbb{Z}_m^{\mathbb{N}}$ . This work provides a systematic study of both \emph{topological directional entropy} (TDE) within Milnor's geometric framework and \emph{measure-theoretic directional entropy} via the Kolmogorov--Sinai formalism.

Keywords

directional entropy cellular automata topological entropy measure-theoretic entropy semigroup actions

Cite

@article{arxiv.2505.10428,
  title  = {A Study of Directional Entropy Arising from \(\mathbb{Z} \times \mathbb{Z}_+\) Semigroup Actions},
  author = {Hasan Akin},
  journal= {arXiv preprint arXiv:2505.10428},
  year   = {2025}
}

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28 pages

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