A Study of Directional Entropy Arising from \(\mathbb{Z} \times \mathbb{Z}_+\) Semigroup Actions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
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| _version_ | 1866910946385985536 |
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| author | Akin, Hasan |
| author_facet | Akin, Hasan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Study of Directional Entropy Arising from \(\mathbb{Z} \times \mathbb{Z}_+\) Semigroup Actions Akin, Hasan Dynamical Systems 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. |
| title | A Study of Directional Entropy Arising from \(\mathbb{Z} \times \mathbb{Z}_+\) Semigroup Actions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2505.10428 |