关于两种混沌映射的有限乘积性质

首先在一般度量空间上给出有限积映射是Li-Yorke混沌的一个判据,并且用反倒展示:当有限积映射是Li-Yorke混沌时,未必一定存在因子映射是Li-Yorke混沌的.然后,利用上述判据,在[0,1]N上证明有限积映射有不可数scrsmbled集的一个充要条件.进而,推出关于有限积映射为Li-Yorke 混沌的一组等价...

On finite-product properties of two kinds of chaotic mappings

In this paper,a criterion is firstly given for finite-product mappings to be chaotic in the sense of Li-Yorke in general metric space. And a counterexample is given to show that a finite-product mapping is chaoticin the sense of Li-Yorke,but its all factor-maps are not.By using the above criterion,a sufficient and necessary condition is proved about a finite product map has an uncountable scrambled set defined on [0,1]N.Moreover,a group of equivalent characterizations of Li-Yorke chaos is obtained.Finally,it is shown that the finite-product property of Devaney chaos is opposite to the one of Li-Yorke chaos,i.e.,the following result is prove that if afinite-product map is Devaney chaotic,then its all factor-maps of a finite-product map are Devaney chaotic,andconversely,not really.