A quantitative shrinking target result on Sturmian sequences for\n rotations

2018/02/05 by Jon Chaika, Chaika, Jon, David Constantine +1
Computer Science · Materials Science · Mathematics · #371A05 #37B10 #37E10 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1802.01370

openalex publication_date 2018/02/05 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28

Abstract

Let R_\α be an irrational rotation of the circle, and code the orbit of\nany point x by whether R_\αⁱ(x) belongs to [0,\α) or\n[\α,1) -- this produces a Sturmian sequence. A point is undetermined at\nstep j if its coding up to time j does not determine its coding at time\nj+1. We prove a pair of results on the asymptotic frequency of a point being\nundetermined, for full measure sets of \α and x.\n

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