On symbolic factors of S-adic subshifts of finite topological rank

2020/12/01 by Bastián Espinoza, Bastíán Espinoza, Espinoza, Bastián
Computer Science · Mathematics · #37B10 #Cellular Automata and Applications #Coding theory and cryptography #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #msc:37B10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2012.00715

Duplicate of arXiv:2008.13689

openalex publication_date 2020/12/01 · arxiv created 2022/02/06 · arxiv updated 2022/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies several aspects of symbolic factors of S-adic subshifts of finite alphabet rank. First, we address a problem raised in [DDPM20] about the topological rank of symbolic factors of S-adic subshifts and prove that this rank is at most the one of the extension system, improving results from [E20] and [GH2020]. As a consequence of our methods, we prove that finite topological rank systems are coalescent. Second, we investigate the structure of fibers π^-1(y) of factor maps π\colon(X,T)→(Y,T) between minimal S-adic subshifts of finite alphabet rank and show that they have the same finite cardinality for all y in a residual subset of Y. Finally, we prove that the number of symbolic factors (up to conjugacy) of a fixed subshift of finite topological rank is finite, thus extending Durand's similar theorem on linearly recurrent subshifts.

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