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arXiv · 1309.3960

Beyond substitutive dynamical systems: S-adic expansions

Valérie Berthé·Vincent Delecroix
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Abstract

An S-adic expansion of an infinite word is a way of writing it as the limit of an infinite product of substitutions (i.e., morphisms of a free monoid). Such a description is related to continued fraction expansions of numbers and vectors. A fundamental example of this relation is between Sturmian sequences and regular continued fractions. We study S-adic words from different perspectives, namely word combinatorics, ergodic theory, and Diophantine approximation, by stressing the parallel with continued fraction expansions.

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Valérie Berthé, Vincent Delecroix. 2013-09-16. Beyond substitutive dynamical systems: S-adic expansions. https://arxiv.org/abs/1309.3960

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