Abstract We present details of a work aiming at the overestimation of Lyapunov exponents defined by the geodesic deviation equations in the previous work. The geodesic deviation vector with post-stabilization is used to compute the fast Lyapunov indicator, considered to be a very sensitive tool for discrimination between ordered or weakly chaotic motions. We make a detailed study of the dynamics in the superposed Weyl field between a black hole and shell of octopoles by using the fast Lyapunov indicator with the Poincaré surface of section. In particular, we examine the effects on the dynamics around the fixed points, of varying one of the three parameters (specific energy E, specific angular momentum L and octopolar moment ), while keeping the other two fixed, and identify the intervals of the varying parameter where the motion is regular or chaotic.
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