Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps
Dynamical Systems
2019-10-22 v2 Classical Analysis and ODEs
Abstract
We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The convergence rate depends explicitly on the modulus of continuity of the observable and on the arithmetic properties of the frequency defining the transformation. Furthermore, we show that for the one dimensional torus translation, these estimates are nearly optimal.
Keywords
Cite
@article{arxiv.1906.07256,
title = {Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps},
author = {Silvius Klein and Xiao-Chuan Liu and Aline Melo},
journal= {arXiv preprint arXiv:1906.07256},
year = {2019}
}
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23 pages