Power Systems Such As Degree Of Continuity

Equicontinuity is a much strong form of stability in topological dynamical systems.It plays a very important role in exploring mapping's sensitivety to initial conditions,topolo-gical transitivity and minimal set etc.The paper is organized as follows:In chapterl, we firstly retrospect the background as well as the status of topological dynamical system and the hyperspace dynamical systems. Then we gave a general framework for dynamical systems research.In chapter 2, As the space is different, we discussed the relationship of equicontinuity between topological dynamical system and induced hyperspace dynamical system. When the base is compact metric space, then the topological dynamical system is equicontinuity if and only if its induced hyperspace system is equicintinuity. When the base is locally compact and second countable metric space, equicontinuity is uniformly topological conjugacy. If the hyperspace dynamical system is equicontinuity, then the base dynamical system is equicontinuity. Under certain conditions, if the dynamical system is eqicontinuity, then the induced hyperspace dynamical system is equicontinuity.