On the equivalence of four chaotic operators

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• 作者：Xinxing  ; Wu  ; ;   ; ^a ;   ; ^{wuxinxing5201314@163.com} ; Peiyong  ; Zhu^a ;   ; ^{zpy6940@sina.com.cn}
• 关键词：Li&ndash ; Yorke chaos ; Li&ndash ; Yorke sensitivity ; Spatio-temporal chaos ; Distributional chaos in a sequence ; Irregular vector ; Bounded operator
• 刊名：Applied Mathematics Letters
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：25
• 期：3
• 页码：545-549
• 全文大小：219 K

文摘

In this paper, we study chaos for bounded operators on Banach spaces. First, it is proved that, for a bounded operator defined on a Banach space, Li¨CYorke chaos, Li¨CYorke sensitivity, spatio-temporal chaos, and distributional chaos in a sequence are equivalent, and they are all strictly stronger than sensitivity. Next, we show that is sensitive dependence iff . Finally, the following results are obtained: (1) is chaotic iff is chaotic for each . (2) The product operator is chaotic iff is chaotic for some .