S - adic expansions related to continued fractions
نویسنده
چکیده
We consider S-adic expansions associated with continued fraction algorithms, where an S-adic expansion corresponds to an infinite composition of substitutions. Recall that a substitution is a morphism of the free monoid. We focus in particular on the substitutions associated with regular continued fractions (Sturmian substitutions), and with Arnoux–Rauzy, Brun, and Jacobi–Perron (multidimensional) continued fraction algorithms. We also discuss the spectral properties of the associated symbolic dynamical systems under a Pisot type assumption.
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