  Bars in galaxies are mainly supported by particles trapped around closed
periodic orbits. These orbits respond to the bar's forcing frequency only and
lack free oscillations. We show that a similar situation takes place in double
bars: particles get trapped around orbits which only respond to the forcing
from the two bars and lack free oscillations. We find that writing the
successive positions of a particle on such an orbit every time the bars align
generates a closed curve, which we call a loop. Loops allow us to verify
consistency of the potential. As maps of doubly periodic orbits, loops can be
used to search the phase-space in double bars in order to determine the
fraction occupied by ordered motions.
