Beyond substitutive dynamical systems: S-adic expansions

2013/09/30 by Valérie Berthé, Vincent Delecroix · 2 citations
Mathematics · #math.DS #math.CO #msc:37B10

paper · pdf

published as RIMS Kôkyûroku Bessatsu B46 (2014) p. 81-123 · 30 pages

arxiv created 2017/07/18 · arxiv updated 2017/07/19

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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