Dynamically possible pattern speeds of double bars
  The method to study oscillating potentials of double bars, based on invariant
loops, is introduced here in a new way, intended to be more intelligible. Using
this method, I show how the orbital structure of a double-barred galaxy (nested
bars) changes with the variation of nuclear bar's pattern speed. Not all
pattern speeds are allowed when the inner bar rotates in the same direction as
the outer bar. Below certain minimum pattern speed orbital support for the
inner bar abruptly disappears, while high values of this speed lead to loops
that are increasingly round. For values between these two extremes, loops
supporting the inner bar extend further out as its pattern speed decreases, and
they become more eccentric and pulsate more. These findings do not apply to
counter-rotating inner bars.
