Positive upper density points and chaos

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• 作者：Yin Jiandong^a ; ^{yjdaxf@163.com} ; Zhou Zouling^b ; ^{lnszzl@mail.sysu.edu.cn}
• 关键词：measure center ; E-system ; chaos
• 刊名：Acta Mathematica Scientia
• 出版年：2012
• 期刊代码：1_02529602
• 类别：mt
• 出版时间：July, 2012
• 卷：32
• 期：4
• 页码：1408-1414
• 文件大小：274 K

摘要

In this work, we mainly investigate the problem of complexity for a topologically dynamical system (X, f). We prove that f has a full measure center if there exists a countable base of X satisfying that, for any i, there is y in X such that N (y, U_i) is a positive Banach upper density set. Moreover, we consider the chaotic property of (X, f). We show that such a system is chaotic in the sense of Takens-Ruelle if it is transitive but not minimal.