Entropy for symbolic dynamics with overlapping alphabets

2010/11/15 by Fabio Drucker, Drucker, Fabio, David Richeson +3
Computer Science · Mathematics · #37B10 #37B40 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1011.3402

openalex publication_date 2010/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of entropies of (standard) full shifts. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.

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