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

Fabien Durand; Alejandro Maass

doi:10.3934/dcds.2003.9.745

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2003, Volume 9, Issue 3: 745-750. Doi: 10.3934/dcds.2003.9.745

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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
2.
Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 UCHILE-CNRS, Universidad de Chile, Casilla 170/3 correo 3, Santiago

Received: February 28, 2002

Revised: November 30, 2002

Published: April 2003

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Abstract

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.

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Mathematics Subject Classification: Primary: 54H20; Secondary: 37B20.

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