  A large fraction of barred galaxies host secondary bars that are embedded in
their large-scale primary counterparts. These are common also in gas poor
early-type barred galaxies. The evolution of such double-barred galaxies is
still not well understood, partly because of a lack of realistic $N$-body
models with which to study them. Here we report a new mechanism for generating
such systems, namely the presence of rotating pseudo-bulges. We demonstate with
high mass and force resolution collisionless $N$-body simulations that
long-lived secondary bars can form spontaneously without requiring gas,
contrary to previous claims. We find that secondary bars rotate faster than
primary ones. The rotation is not, however, rigid: the secondary bars pulsate,
with their amplitude and pattern speed oscillating as they rotate through the
primary bars. This self-consistent study supports previous work based on
orbital analysis in the potential of two rigidly rotating bars. The pulsating
nature of secondary bars may have important implications for understanding the
central region of double-barred galaxies.
