I am interested in the following type of problem:
$M$ is a open manifold and $\mu$ an infinite measure on $M$ that is absolutely continuous with respect to the Lebesgue measure. I consider a complete smooth vector field $X$ on $M$ whose flow preserves $\mu$.
I want to evaluate the measure of the set of recurrent points.
For instance, I could suppose that there are (open) zones of $M$ that are traps: every point of such a zone is taken by the flow to infinity.
I was wondering if there was a literature that dealt with this sort of problems.
Thanks!
