On the Recurrence of Birkhoff Sums for a Circle Rotation and a Hölder Function

Theory of Probability and Its Applications 2026

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Authors: A. V. Kochergin
DOI: 10.1137/s0040585x97t992628
Cited by: 1
References: 18

Abstract

We consider a zero-mean Hölder function on the circle. If an irrational rotation of the circle is sufficiently well approximable by rational rotations, then the sequence of values of the Birkhoff sums remains finite at each point of the circle.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Mathematical functions and polynomials Polynomial and algebraic computation

Publication details

Journal / source
Theory of Probability and Its Applications
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Volume
70
Issue
4
Pages
584–592
Publication date
1 February 2026
Language
EN