Fast and slow points of Birkhoff sums

2019/01/11 by Bayart, Frédéric, Buczolich, Zoltan, Heurteaux, Yanick
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.03504

Abstract

We investigate the growth rate of the Birkhoff sums S_n,α f(x)=∑_k=0^n-1 f(x+kα), where f is a continuous function with zero mean defined on the unit circle \mathbb T and (α,x) is a "typical" element of \mathbb T². The answer depends on the meaning given to the word "typical". Part of the work will be done in a more general context.

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