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Geodesic laminations as geometric realizations of Pisot substitutions

Published online by Cambridge University Press:  01 August 2000

VÍCTOR F. SIRVENT
VÍCTOR F. SIRVENT
Affiliation:
Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas 1086-A, Venezuela (e-mail: vsirvent@usb.ve)
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Abstract

We construct a geodesic lamination on the hyperbolic disk and a dynamical system defined on this lamination. We prove that this dynamical system is a geometrical realization of the symbolic dynamical system that arises from the following Pisot substitution: $1\rightarrow 12, \dotsc, (n-1) \rightarrow 1n, n\rightarrow 1$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 4 , August 2000 , pp. 1253 - 1266
Copyright
2000 Cambridge University Press

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