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

Fabien Durand (1) , Alejandro Maass (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

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.

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Alejandro Maass. A note on limit laws for minimal Cantor systems with infinite periodic spectrum. Discrete and Continuous Dynamical Systems - Series A, 2003, 9 (3), pp.745-750. ⟨10.3934/dcds.2003.9.745⟩. ⟨hal-02465499⟩