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| HAL : inria-00178799, version 1 |
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| Annales de l'Institut Fourier 56, 7 (2006) 2161-2212 |
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| Fractal representation of the attractive lamination of an automorphism of the free group |
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| Pierre Arnoux 1Valerie Berthe 2 |
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| (2006) |
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| In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers ({\it iwip}) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination is, in this case, proved to be measure-theoretically isomorphic to a domain exchange on a self-similar Euclidean compact set. This set is called the central tile of the automorphism, and is inspired by Rauzy fractals associated with Pisot primitive substitutions. The central tile admits some specific symmetries, and is conjectured under the Pisot hypothesis to be a fundamental domain for a toral translation. |
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| 1 : | Institut de mathématiques de Luminy (IML) |
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CNRS : UMR6206 – Université de la Méditerranée - Aix-Marseille II |
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| 2 : | Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM) |
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CNRS : UMR5506 – Université Montpellier II - Sciences et techniques |
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| 3 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 4 : | SYMBIOSE (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – Université de Rennes 1 |
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| INFO/ARITH |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00178799, version 1 | |
| http://hal.inria.fr/inria-00178799 | |
| oai:hal.inria.fr:inria-00178799 | |
| Contributeur : Anne Siegel | |
| Soumis le : Vendredi 12 Octobre 2007, 11:35:05 | |
| Dernière modification le : Lundi 14 Janvier 2008, 15:12:01 | |
