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Arithmetic and dynamical properties of the Rauzy fractal. (Propriétés arithmétiques et dynamiques du fractal de Rauzy.) (French) Zbl 0918.11048

Explicit measure-theoretic isomorphisms are constructed between the symbolic system associated to the substitution \( \sigma_k:0\mapsto 01, 1\mapsto 02,\dots, k-1\mapsto 0k,k\mapsto 0\) for \(k>2\) and a rotation of the torus, and between the adic stationary system associated to the same substitution and the same rotation. Further, it is shown that the two isomorphisms are continuous everywhere. The proofs involve a careful analysis of the boundary of the fractal set introduced by G. Rauzy [Bull. Soc. Math. Fr. 110, 147-178 (1982; Zbl 0522.10032)].

MSC:

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
37B99 Topological dynamics
28A80 Fractals

Citations:

Zbl 0522.10032

References:

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