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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

Fabien Durand 1, and  Alejandro Maass 2,

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.
Keywords: minimal Cantor systems., Bratteli diagrams, Limit laws.
Mathematics Subject Classification: Primary: 54H20; Secondary: 37B2.
Citation: Fabien Durand, Alejandro Maass. A note on limit laws for minimal Cantor systems with infinite periodic spectrum. Discrete & Continuous Dynamical Systems, 2003, 9 (3) : 745-750. doi: 10.3934/dcds.2003.9.745
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