2020/05/25 by N. Pytheas Fogg, Camille Noûs, Fogg, N. Pytheas +2
Computer Science · Mathematics · #11K50 #28A80 #37B10 (Primary) #37D25 #37E05 #37E20 #68R15 (Secondary) #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #cs.FL #math.DS #math.NT #msc:11K50 #msc:28A80 #msc:37B10 #msc:37D25 #msc:37E05 #msc:37E20 #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2005.12229
arxiv created 2020/05/25 · openalex publication_date 2020/05/25 · arxiv updated 2020/05/26 · openalex created_date 2020/05/29 · openalex updated_date 2026/07/28
In this paper, we prove that almost every translation of \mathbbT2 admits a symbolic coding which has linear complexity 2n+1. The partitions are constructed with Rauzy fractals associated with sequences of substitutions, which are produced by a particular extended continued fraction algorithm in projective dimension 2. More generally, in dimension d≥ 1, we study extended measured continued fraction algorithms, which associate to each direction a subshift generated by substitutions, called S-adic subshift. We give some conditions which imply the existence, for almost every direction, of a translation of the torus \mathbbTd and a nice generating partition, such that the associated coding is a conjugacy with the subshift.