The Multi-sensitivity and Topological Sequence Entropy of Dynamical System with Group Action.

In this paper, we study the relationship between the multi-sensitivity and the topological maximal sequence entropy of dynamical systems for general group action. Furthermore, we also discuss the consistency of multi-sensitivity of a dynamical system (G ↷ X) and its hyperspace dynamical system G ↷ K(X). Moreover, we research the relationship between the multi-sensitivity of two dynamical systems and the multi-sensitivity of their product space dynamical system. Finally, we prove that if the topological sequence entropy of G ↷ X vanishes, then so does that of its induced system G ↷ ℳ (X) ; if the topological sequence entropy of G ↷ X is positive, then that of its induced system G ↷ ℳ (X) is infinity. [ABSTRACT FROM AUTHOR]