Study On The Dynamic Characters Of Mappings—Devaney Chaos

This paper studies the compact system (X, f) of Devaney chaotic characters.three conditions of Devaney chaos are changed, and then we get different of Devaneychaos. Because in the three conditions of Devaney chaos, the first condition can not bedecomposed, namely the Devaney chaos chaotic system can be decomposed into twosubsystems,the second conditions describes the system without periodic points is notDevaney chaos system, the third conditions describes the system cannot be predicted,the initial value of small change leads that the iterative results have varied considerably.In the first chapter of this paper discusses Devaney chaos and its modificationof Devaney chaos. To construct the symbol space, it is proved that it is a compactmetric space, using the learned knowledge and some nature of symbolic space,we proofthe symbol space is Devaney chaos.The studing of Set valued dynamical system isactually the movement characteristics of the subset,in the demography, attractor, andmany fields, knowing the movement characters of the subset is very important, soresearching of the set valued dynamical system is very important. Because the symbolspace periodic density contains its set value dynamic system of dense, topologicaltransitivity contains topology delivery of set valued dynamical system, then the setvalued dynamical system of symbol space is Devaney chaos. Due to the topologicalSemi-conjugacy maintain topological mixing invariant, topological mixing containstransitivity and sensitive dependence on initial conditions, then the topologicalSemi-conjugacy maintain modification of Devaney chaotic invariant.The second chapter discusses the modification of weak Devaney chaos. Whenthe sensitive dependence on initial conditions changes weakly sensitive dependence on initial value, a modification of the Devaney chaos changs to modify the weakDevaney chaos. We mainly discuss inverse limit space of the compact system, becausethe topological transitive contains topological transitive of inverse limit space,topologically mixing contains sensitive dependence on initial conditions, is weaklysensitive dependence on initial conditions, using the learned knowledge, we show thatthe inverse limit space is weakly sensitive dependence on initial conditions, even if themodifications of the weak Devaney chaos. As when we discuss Devaney chaos,topological transitivity is less than not, so topological transitivity system has become animportant research object. Because topological dynamical system is not to betopologically transitive, but there must be topologically transitive subsystem.In the third chapter, we construct a new collection of the symbol space, constructa new system that is a strong Devaney chaos.This paper discusses the corresponding change of the three conditions ofDevaney chaos,we get different Devaney chaos. That allows us to research the map ofthe dynamic properties of Devaney chaos more convenientiy, more thorough.