2022/04/13 by Hasan Akın, Chunlin Liu, Akın, Hasan +1
Computer Science · Mathematics · #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2204.06405
openalex publication_date 2022/04/13 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28
In this short paper, we compute the directional sequence entropy for of ℤ+× ℤ-actions generated by cellular automata and the shift map. Meanwhile, we study the directional dynamics of this system. As a corollary, we prove that there exists a sequence such that for any direction, some of the systems above have positive directional sequence entropy. Moreover, with help of mean ergodic theory for directional weak mixing systems, we obtain a result of number theory about combinatorial numbers.