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We study the dynamical interaction of a black hole or central mass concentration with the inner regions of a rapidly rotating barred galaxy. Stochastic regions appear as the central mass is increased. These are associated with the appearance and outward movement of an inner Linblad resonance related to an increase of central mass. The fundamental family of orbits sustaining the bar will dissolve at approximately the point where this resonance reaches the end of the bar. More elongated bars dissolve more easily and orbits closer to the center become stochastic more readily.
Hasan et al. (Sat,) studied this question.