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Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps
Published online by Cambridge University Press: 06 October 2020
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.
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- © The Author(s), 2020. Published by Cambridge University Press
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