2023/10/09 by Hajime Kaneko, Kaneko, Hajime, Wolfgang Steiner +1
Mathematics · Computer Science · Materials Science · #Mathematical Dynamics and Fractals #semigroups and automata theory #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2310.05454
For the Lagrange spectrum and other applications, we determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order, and its solution is the fixed point of a substitution for the alternating lexicographic order. For orders defined by cylinders, we show that the solutions are S-adic sequences, where S is a certain infinite set of substitutions that includes Sturmian morphisms. We also consider a similar problem for symmetric ternary shifts, which is applicable to the multiplicative version of the Markoff-Lagrange spectrum.