Arithmetic and dynamical properties of the Rauzy fractal
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 \textit{G. Rauzy} [Bull. Soc. Math. Fr. 110, 147-178 (1982; Zbl 0522.10032)].
scientific article; zbMATH DE number 1229652
scientific article