  Starting from a Pfaffian equation in dimension $N$ and focusing on compact
solutions for it, we place in perspective the variational method used in [29]
to solve Hilbert's 16th problem. In addition to exploring how this viewpoint
can help in detecting and finding approximations for limit cycles of planar
systems, we recall some of the initial important facts of the full program
developed in [29] to motivate that the same proposal could eventually be used
in other situations. In particular, we make some initial interesting
calculations in dimension $N=3$ that lead to some similar initial conclusions
as with the case $N=2$.
