Interactions between dynamics, arithmetics and combinatorics: the good, the bad, and the ugly

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Languages of k‐interval exchange transformations (2008, background): “This question was of huge interest to word combinatorists who were attempting to classify the systems of low complexity: they tried to generalize the Sturmian sequences by defining several classes of sequences and systems (see [3]) but, up to now, no complete correspondence between sequences and sys”
Topological Properties of Rauzy Fractals (2010, background): “This refers to what is called Rauzy program in [36]: “find generalizations of the Sturmian/rotation interaction which would naturally generate approximation algorithms”.”
Beyond substitutive dynamical systems: S-adic expansions (2013, background): “For more on this subject, see also [32, 54, 61].”