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Dynamical generalizations of the lagrange spectrum

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Abstract

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, three-interval exchanges, and Arnoux-Rauzy systems. The sets of values of these invariants for a given family of systems generalize the Lagrange spectrum, which is what we obtain for the family of rotations with the upper limit of 1/ne n.

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy CNRS — UMR 6206, Case 907, 163 av. de Luminy, F13288, Marseille Cedex 9, France

    Sébastien Ferenczi

  2. Fédération de Recherche des Unités de Mathématiques de Marseille CNRS — FR 2291, Paris, France

    Sébastien Ferenczi

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  1. Sébastien Ferenczi
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Correspondence to Sébastien Ferenczi.

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Ferenczi, S. Dynamical generalizations of the lagrange spectrum. JAMA 118, 19–53 (2012). https://doi.org/10.1007/s11854-012-0028-0

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  • DOI: https://doi.org/10.1007/s11854-012-0028-0

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