  Bars in galaxies are mainly supported by particles trapped around stable
periodic orbits. These orbits represent oscillatory motion with only one
frequency, which is the bar driving frequency, and miss free oscillations. We
show that a similar situation takes place in double bars: particles get trapped
around parent orbits, which in this case represent oscillatory motion with two
frequencies of driving by the two bars, and which also lack free oscillations.
Thus the parent orbits, which constitute the backbone of an oscillating
potential of two independently rotating bars, are the double-frequency orbits.
These orbits do not close in any reference frame, but they map onto loops,
first introduced by Maciejewski & Sparke (1997). Trajectories trapped around
the parent double-frequency orbit map onto a set of points confined within a
ring surrounding the loop.
