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arxiv 2505.10428 v1 pith:EFS2PBHR submitted 2025-05-15 math.DS

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

Hasan Akin This is my paper
classification math.DS
keywords directionalentropymathbbactionsemphsemigrouparisingautomata
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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.

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