Study On Related Dynamic Properties Of Hyperspace Systems Under The Condition Of Strong Uniform Convergence

The main content of this paper is that the relationship between the sequence mapping and the limit mapping is studied by strong uniform convergence on hyperspace.The content of the article are as follows:The second chapter is inspired by the idea of the document[13]and[11].The def-inition of strong uniform convergence is introduced on hyperspace.Then,making use of the definition discusses the relationship between sensitive dependence on initial condi-tion,equicontinuity,periodic point and almost periodic point of the sequence mapping and sensitive dependence on initial condition,equicontinuity,periodic point and almost periodic point of the limit mapping on hyperspace.The third chapter,on the basis of the second chapter,discusses the relationship between the sequence mapping and the limit mapping in Li-Yorke chaos,Li-Yorke-? chaos and Distributional chaos on hyperspace.The fourth chapter is inspired by the idea of the document[17].Firstly,the definition of strong Kato*chaos is given.Next,The author studies the implicative relationship between strong Kato*chaos of the hyperspace dynamical system and strong Kato*chaos of the base space dynamic system.