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 {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.
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.
基金
financially supported by the Foundation(GJJ11295) from the Education Department of Jiangxi
