A Study of Directional Entropy Arising from \(ℤ × ℤ₊\) Semigroup Actions

2025/05/15 by Hasan Akın, Akin, Hasan
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2505.10428

openalex publication_date 2025/05/15 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

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 ℤ_m^ℕ. This work provides a systematic study of both topological directional entropy (TDE) within Milnor's geometric framework and measure-theoretic directional entropy via the Kolmogorov--Sinai formalism.

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