  We consider planar vector field without zeroes X and study the image of the
associated Lie derivative operator LX acting on the space of smooth functions.
We show that the cokernel of LX is infinite-dimensional as soon as X is not
topologically conjugate to a constant vector field and that, if the topology of
the integral trajectories of X is ``simple enough'' (e.g. if X is polynomial)
then X is transversal to a Hamiltonian foliation. We use this fact to find a
large explicit subalgebra of the image of LX and to build an embedding of R^2
into R^4 which rectifies X. Finally we use this embedding to characterize the
functions in the image of LX.
