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published on March 22, 2024
A reasonably-sized morphism giving Abelian critical exponent less than 2
By James D. Currie
Renormalisation via continued fractions in symbolic dynamics
We show how to construct 'simple' symbolic dynamical systems in terms of renormalisation schemes associated with multidimensional continued fractions. Continued fractions are used here to generate infinite words thanks to the iteration of infinite sequences of substitutions. Simple means that these symbolic systems have a linear number of factors of a given length, or that they have pure discrete spectrum, or else, that they have a low symbolic discrepancy. We also discuss the relation between these notions.
