Birkhoff sum fluctuations in substitution dynamical systems
Dynamical Systems
2015-05-07 v1 Combinatorics
Probability
Abstract
We consider the deviation of Birkhoff sums along fixed orbits of substitution dynamical systems. We show distributional convergence for the Birkhoff sums of eigenfunctions of the substitution matrix. For noncoboundary eigenfunctions with eigenvalue of modulus 1, we obtain a central limit theorem. For other eigenfunctions, we show convergence to distributions supported on Cantor sets. We also give a new criterion for such an eigenfunction to be a coboundary, as well as a new characterization of substitution dynamical systems with bounded discrepancy
Cite
@article{arxiv.1505.01428,
title = {Birkhoff sum fluctuations in substitution dynamical systems},
author = {Elliot Paquette and Younghwan Son},
journal= {arXiv preprint arXiv:1505.01428},
year = {2015}
}