  We analyze the evolution of stellar bars in galactic disks in mildly triaxial
flat-core and cuspy CDM halos. We use tailored simulations of rigid and live
halos which include the feedback from disk/bar onto the halo in order to test
the work by El-Zant & Shlosman (2002). The latter used the Liapunov exponents
to analyze the fate of bars in analytical asymmetric halos. We find: (1) The
bar growth is similar in all rigid axisymmetric and triaxial halos. (2) Bars in
live models vertically buckle and form a pseudobulge with a boxy/peanut shape.
(3) In live axisymmetric halos, the bar strength varies little during the
secular evolution. The bar pattern speed anticorrelates with the halo core
size. The bar strength is larger for smaller disk-to-halo mass ratios within
disk radii, the bar size correlates with the halo core sizes, and the bar
pattern speeds -- with the halo central mass concentration. Bars embedded in
live triaxial halos have a starkly different fate: they dissolve on ~1.5-5 Gyr
due to the onset of chaos over continuous zones, leaving behind a weak oval
distortion. The onset of chaos is related to the halo triaxiality, the fast
rotating bar and the halo cuspiness. Before the bar dissolves, the region
outside it develops strong spiral structures, especially in the live triaxial
halos. (4) More angular momentum is absorbed by the triaxial halos as compared
to the axisymmetric models and its exchange is mediated by resonances. (5)
Cuspy halos are more susceptible than flat-core halos to having their
prolateness washed out by the bar. We analyze these results in terms of the
stability of trajectories and development of chaos. We set constraints on the
triaxiality of DM halos by comparing our predictions to recent observations of
bars out to z~1.
