  We show that stable double-frequency orbits form the backbone of double bars,
because they trap around themselves regular orbits, as stable closed periodic
orbits do in single bars, and in both cases the trapped orbits occupy similar
volume of phase-space. We perform a global search for such stable
double-frequency orbits in a model of double bars by constructing maps of
trajectories with initial conditions well sampled over the available
phase-space. We use the width of a ring sufficient to enclose a given map as
the indicator of how tightly the trajectory is trapped around a
double-frequency orbit. We construct histograms of these ring widths in order
to determine the fraction of phase-space occupied by ordered motions. We build
22 further models of double bars, and we construct histograms showing the
fraction of the phase-space occupied by regular orbits in each model. Our
models indicate that resonant coupling between the bars may not be the dominant
factor reducing chaos in the system.
