Limit laws of entrance times for low complexity Cantor minimal systems

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]

This paper is devoted to the study of limit laws of entrance times to cylinder sets for Cantor minimal systems of zero entropy using their representation by means of ordered Bratteli diagrams. We study in detail substitution subshifts and we prove these limit laws are piecewise linear functions. The same kind of results is obtained for classical low complexity systems given by non stationary ordered Bratteli diagrams.

Mots clés: limit laws; substitution; entrance times; return times; Bratteli diagrams

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Alejandro Maass. Limit laws of entrance times for low complexity Cantor minimal systems. Nonlinearity, 2001, 14, pp.683-700. ⟨hal-00309040⟩