  We investigate the stability of trajectories in barred galaxies with mildly
triaxial halos by means of Liapunov exponents. This method is perfectly
suitable for time-dependent 3D potentials where surfaces of sections and other
simple diagnostics are not applicable. We find that when halos are
centrally-concentrated most trajectories starting near the plane containing the
bar become chaotic. Moreover, the shape of many of the remaining regular
trajectories do not match the bar density distribution, being too round.
Therefore, time-independent self-consistent solutions are highly unlikely to be
found. When the non-rotating non-axisymmetric perturbation in the potential
reaches 10%, almost all trajectories integrated are chaotic and have large
Liapunov exponents. No regular trajectories aligned with the bar have been
found. Hence, if the evolution of the density figure is directly related to the
characteristic timescale of orbital instability, bar dissolution would take
place on a timescale of few dynamical times. The slowly rotating
non-axisymmetric contribution to the potential required for the onset of
widespread chaotic behavior is remarkably small. Systems consisting of
centrally-concentrated axisymmetric halos and stellar bars thus appear to be
structurally unstable, and small (1%) deviations from perfect axisymmetry
should result in a bar dissolution on a timescale significantly smaller than
the Hubble time. Since halos found in CDM simulations of large scale structure
are both centrally-concentrated and triaxial it is unlikely that stellar bars
embedded in such halos would form and survive unless the halos are modified
during the formation of the baryonic component.
