Abstract
We consider a family of minimal sequences on a $3$-symbol alphabet with complexity $2n+1$, which satisfy a special combinatorial property. These sequences were originally defined by P. Arnoux and G. Rauzy as a generalization of the binary sturmian sequences. We prove that the dynamical system associated to each of these sequences of this family, can be realized as a dynamical system defined on a geodesic lamination on the hyperbolic disk. This is a generalization of the results shown in a previous paper of the author. We also show some applications of these results.
Citation
Victor F. Sirvent. "Geodesic laminations as geometric realizations of Arnoux--Rauzy sequences." Bull. Belg. Math. Soc. Simon Stevin 10 (2) 221 - 229, June 2003. https://doi.org/10.36045/bbms/1054818025
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