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May  2003, 9(3): 745-750. doi: 10.3934/dcds.2003.9.745

A note on limit laws for minimal Cantor systems with infinite periodic spectrum

1. 

Faculté de Mathématiques et d'Informatique et, Laboratoire Amiénois de Mathématiques Fondamentales et Appliquées, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80000 Amiens, France

2. 

Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 UCHILE-CNRS, Universidad de Chile, Casilla 170/3 correo 3, Santiago

Received  March 2002 Revised  December 2002 Published  February 2003

Recently in [6] Y. Lacroix proved that any distribution function can be obtained as a limit law of return time for any ergodic aperiodic system. In this note we provide an alternative construction, based on Bratteli-Vershik representations of systems, which works for any minimal Cantor system having an infinite periodic spectrum. The construction is especially simple for odometers.
Citation: Fabien Durand, Alejandro Maass. A note on limit laws for minimal Cantor systems with infinite periodic spectrum. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 745-750. doi: 10.3934/dcds.2003.9.745
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