Complexity and directional entropy in two dimensions

2014/09/17 by Ryan Broderick, Broderick, Ryan, Van Cyr +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #37B10 #37B40 #Chemical Synthesis and Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1409.5056

openalex publication_date 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the directional entropy of the dynamical system associated to a \Z² configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a \Z² system with the same local assumptions have zero directional entropy.

Citations

• Symbolic Dynamics II. Sturmian Trajectories

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