The sufficient conditions for dynamical systems of semigroup actions to have some stronger forms of sensitivities

In this paper, we introduce several stronger forms of sensitivities in the dynamical systems of semigroup actions, such as thick sensitivity and thickly syndetical sensitivity, and obtain some sufficient conditions for a dynamical system to have such sensitivities. We prove that a weakly mixing system of semigroup actions is thickly sensitive and a minimal weakly mixing system as well as a nonminimal M-system of semigroup actions is thickly syndetically sensitive.