Geodesic laminations as geometric realizations of Arnoux-Rauzy sequences
In [Bull. Soc. Math. Fr. 119, No. 2, 199--214 (1991; Zbl 0789.28011)], \textit{P. Arnoux} and \textit{G. Rauzy} introduced a family of infinite sequences defined over a ternary alphabet which offers a generalization to the well-known family of Sturmian sequences. In the paper under review, the author proves that the symbolic dynamical system associated to each of these sequences can be realized as a geometric dynamical system defined on a geodesic lamination on the hyperbolic disk. The term ``realized'' means that the two dynamical systems are semiconjugate. This generalizes an earlier result of the author [Ergodic Theory Dyn. Syst. 20, No. 4, 1253--1266 (2000; Zbl 0963.37013)] in which he dealt only with the particular case of the Tribonacci sequence.
scientific article; zbMATH DE number 2031043