  The production of quantum entanglement between weakly coupled mapping
systems, whose classical counterparts are both strongly chaotic, is
investigated. In the weak coupling regime, it is shown that time correlation
functions of the unperturbed systems determine the entanglement production. In
particular, we elucidate that the increment of nonlinear parameter of coupled
kicked tops does not accelerate the entanglement production in the strongly
chaotic region. An approach to the dynamical inhibition of entanglement is
suggested.
