Chaotic and topological properties of β-transformations
Chaotic and topological properties of β-transformations
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DOI：
10.1016/j.jmaa.2011.05.049
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发表时间：
2011-11
影响因子：
1.3
通讯作者：
Bing Li;Yi-Chiuan Chen
中科院分区：
文献类型：
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作者：
Bing Li;Yi-Chiuan Chen
本文证明了β变换在Li-yorke和Devaney意义下都是混沌的。研究了具有稠密和非稠密轨道的点集的拓扑和度量性质。我们还证明了β变换下具有非稠密轨道的点集对任何β>；1都是全Hausdorff维的。
In this paper, we prove that the β-transformations are chaotic in the sense of both Li–Yorke and Devaney. The topological and metric properties of the sets of points with dense or non-dense orbits are investigated. We also prove the result that the set of points with non-dense orbits under the β-transformation is of full Hausdorff dimension for any β> 1.