I've got two homeomorphisms $f$ and $g$ such that their lifts are given by
$F(x) = x + \varepsilon \sin( 2 \pi n x)$ and $G(x) = x + \frac{1}{n} + \varepsilon \sin( 2 \pi n x)$, where $0 < \varepsilon < \frac{1}{2 n \pi}$.
Problem: Evaluate number of rotation $f$ and $g$ and find periodic orbits.
First part was easy to me: $\rho(f) = 0$ and $\rho(g) = \frac{1}{n}$, directly by definition and independence of $x$. But I don't know how it corresponds with periodic orbits.