  This paper deals with the asymptotics of the ODE's flow induced by a regular
vector field b on the d-dimensional torus R d /Z d. First, we start by
revisiting the Franks-Misiurewicz theorem which claims that the Herman rotation
set of any two-dimensional continuous flow is a closed line segment of R 2.
Various general examples illustrate this result, among which a complete study
of the Stepanoff flow associated with a vector field b = a $\zeta$, where
$\zeta$ is a constant vector in R 2. Furthermore, several extensions of the
