Chaoticity On Special Spaces

Although nearly all the chaotic definitions are indeterminant in long-term actions, chaotic phenomenon of them are not equal to each other. Different chaotic definitions have different sense in actual analysis.The chaotic analysis on special spaces is meanful. Since the beginning of this century, by the study of the impact of differential inclusions, In 2003 Roman-Flores [3]compared the transitivity problems of compact system and a class of set-valued dynamical system induced by this system, and proved that the transitivity of such set-valued dynamic system implies the transitivity of the whole system,but on the contrary it does not hold. They further proposed the basic problem about chaos, whether does the chaoticity of compact system ( X, f) imply the chaoticity of its induced set-valued system (K ( X ),f),and on the contrary whether does the chaoticity of (K ( X ),f)imply the chaoticity of ( X, f).The main purposes of this paper are as following:1 Firrst of all we give a suffcient condition of distributional chaos in a sequence, Second we discussed distributional chaoticity in a sequence of ( X, f) associated to distributional Chaos in a sequence of (K ( X ),f).2 We consider the CML [1] of the form x_m+1,n=(1-ε)f(x_m,n)+0.5ε{f(x_m,n-1)+f(x_m,n+1)} wherem∈N₀={0,1,2,…,n∈Z={…,-1,0,1,…}ε∈[0,1] is a constant,and f : R→Ris a continouous function.A new definition of chaos on recurrence points set is discrete spatiomporal systems is given and one sufficient condition for this system to be distributively chaotic is derived.