  The Newtonian as well as the special relativistic dynamics are used to study
the stability of orbits of a test particle moving around a black hole plus a
dipolar halo. The black hole is modeled by either the usual monopole potential
or the Paczynki-Wiita pseudo-Newtonian potential. The full general relativistic
similar case is also considered. The Poincare section method and the Lyapunov
characteristic exponents show that the orbits for the pseudo-Newtonian
potential models are more unstable than the corresponding general relativistic
geodesics.
