  We study the semi-classical limits of the first eigenfunction of a positive
second order operator on a compact Riemannian manifold when the diffusion
constant $\epsilon$ goes to zero. We assume that the first order term is given
by a vector field $b$, whose recurrent components are either hyperbolic points
or cycles or two dimensional torii. The limits of the normalized eigenfunctions
concentrate on the recurrent sets of maximal dimension where the topological
pressure \cite{Kifer90} is attained. On the cycles and torii, the limit
measures are absolutely continuous with respect to the invariant probability
measure on these sets. We have determined these limit measures, using a blow-up
analysis.
