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This study explores directional entropy and its topological and measure-theoretic aspects, suggesting new insights into 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 ZₘN. 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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Hasan Akın (2025) studied this question.
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