Testing for the Wada property in a weakly magnetized black hole system

Abstract

Dynamical systems possessing three or more basins of attraction may possess what is known as the Wada property: all points on the boundary of one of the basins are also on the boundary of all of the other basins. One of the ways to test for this property is the merging method. We apply this method to the case of a charged test particle moving in the vicinity of a weakly magnetized black hole. We show that the system is Wada when its orbital angular momentum L_z is anti-aligned with the magnetic field B, but is not if L_z is aligned with B.