Chaotic scattering is usually associated with the transient chaotic dynamics in open Hamiltonian systems, and has been studied for more than two decades because it is relevant to a host of areas in physics such as astrophysics, optics, fluid mechanics, nanophysics, etc., see [1] and the references therein.It is very important to understand what dynamical phenomena are robust and may persist in the presence of various physical perturbations, since factors such as weak dissipations and/or noise may be present in most realistic situations.