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| HAL : hal-00581694, version 1 |
| arXiv : 1103.6181 |
| Fiche détaillée |  Récupérer au format |
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| Dynamics of lambda-continued fractions and beta-shifts |
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| Elise Janvresse 1Benoît Rittaud 2 |
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| (2011) |
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| For a real number $0<\lambda<2$, we introduce a transformation $T_\lambda$ naturally associated to expansion in $\lambda$-continued fraction, for which we also give a geometrical interpretation. The symbolic coding of the orbits of $T_\lambda$ provides an algorithm to expand any positive real number in lambda-continued fraction. We prove the conjugacy between $T_\lambda$ and some beta-shift, $\beta>1$. Some properties of the map $\lambda\mapsto\beta(\lambda)$ are established: It is increasing and continuous from ]0, 2[ onto ]1,\infty[ but non-analytic. |
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| 1 : | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| 2 : | Laboratoire d'Analyse, Géométrie et Applications (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| Domaine | : | Mathématiques/Systèmes dynamiques Mathématiques/Théorie des nombres |
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| continued fractions – $\beta$-expansion |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00581694, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00581694 | |
| oai:hal.archives-ouvertes.fr:hal-00581694 | |
| Contributeur : Elise Janvresse | |
| Soumis le : Jeudi 31 Mars 2011, 15:37:15 | |
| Dernière modification le : Vendredi 1 Avril 2011, 13:10:29 | |
