Nonrecurrence of the integral of a conditionally periodic function (Q1177827)

The author gives examples of conditionally periodic functions \(f(x_ 1,\dots,x_ s)\) such that the integral \(\int^ t_ 0 f(\omega_ 1 t,\dots,\omega_ s t)dt\) is greater than a positive constant \(C\) for all \(t\) greater than \(t_ 0\) under the condition that linearly independent real numbers \(\omega_ 1,\dots,\omega_ s\) over \(\mathbb{Z}\) satisfy some inequalities.