  We prove that the polynomial entropy of an orientation preserving
homeomorphism of the circle equals 1 when the homeomorphism is not conjugate to
a rotation and that it is 0 otherwise. In a second part we prove that the
polynomial entropy of a flow on the two dimensional torus associated with a
$C^1$ nonvanishing vector field is less that $1$. We moreover prove that when
the flow possesses periodic orbits its polynomial entropy equals 1 unless it is
conjugate to a rotation (in this last case, the polynomial entropy is zero).
