C. Gutierrez (IMPA)
Cr-closing for flows on 2-manifolds
For some full measure subset ${\cal B}$ of the set of {\em iet's} (i.e. interval exchange transformations) the following is satisfied:
Let $X$ be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface $M$. Given a nontrivial recurrent point $p\in M$ of $X,$ the holonomy map around $p$ is semi-conjugate to an {\em iet} $E :[0,1) \to [0,1).$ If $E\in {\cal B}$ then there exists a $C^r$ vector field $Y$, arbitrarily close to $X$, in the $C^r-$topology, such that $Y$ has a closed trajectory passing through $p$.
