On a Theorem of Bohl Regarding Integrals of Quasi-Periodic Functions

Abstract

Bohl points of a conditionally periodic motion are defined as the phases such that the integral of a continuous function with zero mean value along the motion is always nonnegative (or nonpositive). Bohl points are known to always exist. This note is devoted to a generalization of this result to the case of uniquely ergodic dynamical systems as well as to almost periodic Bohr functions.