How chaotic is an almost mean equicontinuous system
How chaotic is an almost mean equicontinuous system
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DOI：
10.3934/dcds.2018208
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发表时间：
2018-06
期刊：
影响因子：
--
通讯作者：
Jie-lin Li
中科院分区：
文献类型：
--
作者：
Jie-lin Li
讨论了一个几乎平均等连续系统的混沌性问题。证明了每一个拓扑动力系统都可以嵌入到一个具有相同熵的几乎平均等连续系统中，该系统是某个平均等连续系统的几乎一一扩展。此外，存在一个拓扑K和Devaney混沌的几乎平均等连续系统，由此我们知道，这种拓扑K系统的每一个遍历测度都不具有完全支持。
The question how chaotic is an almost mean equicontinuous system is addressed. It is shown that every topological dynamical system can be embedded into an almost mean equicontinuous system with the same entropy which is an almost one-to-one extension of some mean equicontinuous system. Besides, there is an almost mean equicontinous system that is topologically K and Devaney chaotic, and as this consequence we know that every ergodic measure of such a topologically K system does not have full support.