POSITIVE UPPER DENSITY POINTS AND CHAOS

来源 :数学物理学报(英文版) | 被引量 : 0次 | 上传用户:liongliong445
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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 {Ui}∞i=0 of X satisfying that,for any i,there is y in X such that N(y,Ui) 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.
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