Study On Transitivity?Mixing And Sensitive Dependence Of Hyperspace System In The Sense Of Furstenberg Families

In this paper,we mainly study the transitivity,mixing,and the sensitive dependence of the hyperspace system and the original dynamical system in the sense of Purstenberg families.In the first chapter,we briefly introduce the development of the dynamical system and the hyperspace system,and then introduce the development of Furstenberg families and the general framework of this paper.The second chapter,we discuss the impli-cation of the-transitivity between the original dynamical system and the hyperspace system,we prove that the F-mixing,the F-equicontinuity and the F-equidistance of the original dynamical system and the hyperspace system are equivalent.In addi-tion,we get three equivalent propositions about the F-transitivity and F-mixing of the hyperspace system.In the third chapter,we discuss that the F-sensitivity of the original dynamical system and the hyperspace system is equivalent,and we get four e-quivalent propositions related to F-sensitivity.Finally,we show that the asymptotic sensitivity(F-multiple sensitivity)of the original dynamical system is equivalent to the asymptotic sensitivity(F-multiple sensitivity)of the hyperspace system.