Devaney chaos revisited

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• 作者：Xiaoyi Wang ; Yu Huang ; ^{stshyu@mail.sysu.edu.cn}
• 关键词：54H20 ; 37D45
• 刊名：Topology and its Applications
• 出版年：2013
• 出版时间：15 February, 2013
• 年：2013
• 卷：160
• 期：3
• 页码：455-460
• 全文大小：173 K

文摘

Let X be a metric space, and let be a continuous transformation. In this note, a concept indecomposability of f is introduced. We show that transitivity implies indecomposability and that Devaney chaos is equivalent to indecomposability together with dense periodicity. Moreover, we point out that the indecomposability and the dense periodicity are independent of each other even for interval maps (i.e., neither implies the other).