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We study the transition from regular to chaotic motion in a prolateelliptical galaxy dynamical model with a bulge and a dense nucleus. Ournumerical investigation shows that stars with angular momentum Lz less than orequal to a critical value Lzc, moving near the galactic plane, are scattered tohigher z, when reaching the central region of the galaxy, thus displayingchaotic motion. An inverse square law relationship was found to exist betweenthe radius of the bulge and the critical value Lzc of the angular momentum. Onthe other hand, a linear relationship exists between the mass of the nucleusand Lzc. The numerically obtained results are explained using theoreticalarguments. Our study shows that there are connections between regular orchaotic motion and the physical parameters of the system, such as the star'sangular momentum and mass, the scale length of the nucleus and the radius ofthe bulge. The results are compared with the outcomes of previous work.

The nature of orbits in a prolate elliptical galaxy model with a bulge and a dense nucleus