Symbolic coding of linear complexity for generic translations on the torus, using continued fractions
Résumé
In this paper, we prove that almost every translation on T2 admits a symbolic coding which has linear complexity 2n + 1. The partitions are constructed with Rauzy fractals associated with sequences of substitutions, which are produced by a particular extended continued fraction algorithm in projective dimension 2. More generally, in dimension d ≥ 1, we study extended measured continued fraction algorithms, that associate to each direction a subshift generated by substitutions, called S-adic subshift. We give some conditions which imply the existence, for almost every direction, of a translation on the torus Td and a nice generating partition, such that the associated coding is a measurable conjugacy with the subshift that it defines.
Domaines
Mathématiques [math]| Origine | Fichiers produits par l'(les) auteur(s) |
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