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We study the regular or chaotic nature of motion in a disk galaxy with a dense nucleus and an asymmetric dark halo. Two cases, the 2D model and the 3D model, are investigated. In the 2D model, a considerable fraction of the phase plane is covered by chaotic orbits. Two factors seem to be responsible for the chaotic motion: (i) the dense nucleus and (ii) the asymmetries in the dark halo. Our numerical experiments suggest, that there are several chaotic components on the Poincare phase plane. Different chaotic components are induced by the asymmetries in the halo. Each chaotic component seems to have a different value of the Lyapunov Characteristic Exponent, for small values of the asymmetry parameter and a unique LCE for larger values of the asymmetry parameter. A comparison of the present results with outcomes from previous work is also presented.