Pisot Substitution Conjecture and Rauzy Fractals

2024/01/15 by Nakaishi, Kentaro
#05B45 (Secondary) #11F85 #28A80 #37A30 #37A44 (Primary) 37A25 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.07771

Abstract

We provide a proof for one version of Pisot conjecture. We make use of the weak mixing property of the subshift of finite type derived from the prefix-suffix automaton to conclude that the substitution dynamical system has pure discrete spectrum.

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