Dynamical properties of the Pascal adic transformation
Dynamical Systems
2007-05-23 v1
Abstract
We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the return time to cylinders is given by a step function. We construct a representation of the system by a subshift on a two-symbol alphabet and then prove that the complexity function of this subshift is asymptotic to a cubic, the frequencies of occurrence of blocks behave in a regular manner, and the subshift is topologically weak mixing.
Cite
@article{arxiv.math/0310317,
title = {Dynamical properties of the Pascal adic transformation},
author = {Xavier Mela and Karl Petersen},
journal= {arXiv preprint arXiv:math/0310317},
year = {2007}
}