2023/04/28 by Ibai Aedo, Aedo, Ibai, Uwe Grimm +3
Computer Science · Mathematics · #37B10 #54H15 #Authorship Attribution and Profiling #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2305.00078
openalex publication_date 2023/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the forward limit set Λ of a semigroup S generated by a family of substitutions of a finite alphabet, which typically coincides with the set of all possible s-adic limits of that family. We provide several alternative characterisations of the forward limit set. For instance, we prove that Λ is the unique maximal closed and strongly S-invariant subset of the space of all infinite words, and we prove that it is the closure of the set of images of all fixed points under S. It is usually difficult to compute a forward limit set explicitly; however, we show that, provided certain assumptions hold, Λ is uncountable, and we supply upper bounds on its size in terms of logarithmic Hausdorff dimension.