We investigate the stability properties of trajectories in barred galaxies with mildly triaxial halos by means of Liapunov exponents. This method is perfectly suitable for time-dependent 3-D 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. The spatial density distribution of these orbits does not match that of the bar, being overextended in- and out-of-the plane compared to the latter. Moreover, the shape of many of the remaining regular trajectories do not match the 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. Even
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