Weakly Almost Periodic Points and Some Chaotic Properties of Dynamical Systems
Weakly Almost Periodic Points and Some Chaotic Properties of Dynamical Systems
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DOI：
10.1142/s0218127415501151
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发表时间：
2015-09
期刊：
影响因子：
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通讯作者：
Jiandong Yin;Zuoling Zhou
中科院分区：
文献类型：
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作者：
Jiandong Yin;Zuoling Zhou
设X是一个紧致度量空间, f:X→X是一个连续映射.引入了遍历混沌和强遍历混沌的概念，证明了如果f是可迁的但不是最小的，且具有满测度中心，则f是强遍历混沌的。此外，给出了f为Ruelle-Takens混沌的一些充分条件.例如，我们证明了f是Ruellle-Takens混沌的，如果f是可传递的，并且存在X的可数基，使得对于每个i > 0，Ui关于它自身的相遇时间集N（Ui，Ui）具有大于的较低密度。
Let X be a compact metric space and f : X → X be a continuous map. In this paper, ergodic chaos and strongly ergodic chaos are introduced, and it is proven that f is strongly ergodically chaotic if f is transitive but not minimal and has a full measure center. In addition, some sufficient conditions for f to be Ruelle–Takens chaotic are presented. For instance, we prove that f is Ruelle–Takens chaotic if f is transitive and there exists a countable base of X such that for each i > 0, the meeting time set N(Ui, Ui) for Ui with respect to itself has lower density larger than .