2020/09/03 by James S. Evans, Evans, James
Computer Science · Mathematics · #11B85 (Primary) 42A38 #28A80 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2009.01425
openalex publication_date 2020/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The k-regular sequences exhibit a self-similar behaviour between powers of k. One way to study this self-similarity is to attempt to describe the limiting shape of the sequence using measures, which results in an object which we call the ghost measure. The aim of this paper is to explicitly calculate this measure and some of its properties, including its Lebesgue decomposition, for the general family of affine 2-regular sequences.