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Birkhoff Sum Fluctuations in Substitution Dynamical Systems by Paquette, Elliot; Son, Younghwan is a scholarly article available to read on EtoBox.

What is Birkhoff Sum Fluctuations in Substitution Dynamical Systems about?

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

Author

Paquette, Elliot; Son, Younghwan

Published

2015

Language

EN