Some Reaserch On D_p~q Chaos

Topological entropy and chaos are two basic concepts which describe the com-plexity of dynamical systems. Researchers study the relationship of them on kindsof topological space. They want to know, on a special topological spaces, whethera complex system in the sense of entropy exhibits chaotic phenomenon, or a chaoticsystem has nonzero entropy.D_p^q chaos has been proposed in recent two years, which describes chaotic phe-nomenon from the upper and lower density of the approximate time set of two points.In this thesis, we study the relationship between this kind of chaos and entropy. InChapter Three, we point out a kind of dynamical system（subshifts of finite type） isD_p^q chaotic for any0≤p≤q≤1when it has positive entropy. In Chapter Four, weconstruct a system which is D_1/4^3/4chaotic, but its topological sequence entropy is zeroalong any sequence, say, it’s a null system.