  We investigate the open Closing Lemma problem for vector fields on the
2-dimensional torus. Under the assumption of bounded type rotation number, the
$C^r$ Closing Lemma is verified for smooth vector fields that are
area-preserving at all saddle points. Namely, given such a $C^r$ vector field
$X$, $r\geq 4$, with a non-trivially recurrent point $p$, there exists a vector
field $Y$ arbitrarily near to $X$ in the $C^r$ topology and obtained from $X$
by a twist perturbation, such that $p$ is a periodic point of $Y$.
  The proof relies on a new result in 1-dimensional dynamics on the
non-existence of semi-wandering intervals of smooth maps of the circle.
