Sébastien Ferenczi – Généralisations dynamiques du spectre de Lagrange

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Date(s) - 8 avril 2011

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We compute two invariants of topological conjugacy, the upper and lower limits of the inverse of Boshernitzan’s $ne_n$, where $e_n$ is the smallest measure of a cylinder of length $n$, for three families of symbolic systems, the natural codings of rotations and three-interval exchanges and the Arnoux-Rauzy systems. The sets of values of these invariants for a given family of systems generalize the Lagrange spectrum, which is what we get for the family of rotations with the upper limit of $\frac{1}{ne_n}$.