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