Dependence Of The Initial Research Hyperspace Dynamical System Response And Non-autonomous Dynamical Systems Sensitive

Since both hyperspace dynamical systems and non-autonomous dynamical systems are the important research directions in dynamical systems, when hy-perspace equipped with different topologies, several relationships between them appeared. Jose L. Gomez-Rueda, Alejandro Illanes, Hector Mendez[1] studied some relationships between symmetric products dynamical systems and original dynamical systems. The second chapter of this paper studied the relationships between hyperspace equipped with hit-or-miss topology and original dynamical systems, some new conclusions are obtained. In addition, Xiong Jincheng[2] and Shao song[3] introduced the definitions of n sensitivity to initial conditions and perfect sensitivity to initial conditions in autonomous dynamical systems, so the third chapter of this paper introduced the definitions of n sensitivity to initial conditions and perfect sensitivity to initial conditions in non-autonomous dy-namical systems, and studied the properties of them. Then the innovations of the paper are structured as follows:In chapter2, Motivated by the ideas of professor Jose L., Gomez-Rueda, Alejandro Illanes, Hector Mendez. Firstly, the definitions of co-compact point transitivity and weak topological transitivity arc introduced, then some exam-ples arc provided to show the relationships between co-compact point transi-tivity and point transitivity, weak topological transitivity and topological tran-sitivity. In addition, the authors study the relationships between co-compact point transitivity, recurrent point, almost period point and topological exact of original dynamical systems (X,f) respectively and transitivity point, recur-rent point, almost period point and topological exact of hyperspace dynamical systems (2x,p,2f). In chapter3, Motivated by the ideas of professor Xiong and Shao, the defi-nitions of n sensitivity to initial conditions and perfect sensitivity to initial con-ditions are introduced in non-autonomous dynamical systems, and we discussed the properties of them.