Limit laws of entrance times for low complexity Cantor minimal systems

TL;DR

This paper investigates the statistical behavior of entrance times in low complexity Cantor minimal systems, revealing that their limit laws are piecewise linear functions, especially in substitution subshifts and non-stationary Bratteli diagram systems.

Contribution

It provides a detailed analysis of limit laws of entrance times for low entropy systems using ordered Bratteli diagrams, highlighting their piecewise linear nature.

Findings

Limit laws are piecewise linear functions for substitution subshifts.

Results extend to classical low complexity systems with non-stationary diagrams.

Enhanced understanding of entrance time distributions in minimal Cantor systems.

Abstract

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.