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題名: | Tree-shifts: Irreducibility, mixing, and the chaos of tree-shifts | 作者: | 班榮超 Ban, Jung-Chao Chang, Chih-Hung |
貢獻者: | 應數系 | 日期: | 五月-2017 | 上傳時間: | 27-五月-2020 | 摘要: | Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems, is difficult and only a few results have been obtained so far. \nThis paper studies shifts defined on infinite trees, which are called tree-shifts. Infinite trees have a natural structure of one-sided symbolic dynamical systems equipped with multiple shift maps and constitute an intermediate class between one-sided shifts and multidimensional shifts. We have shown not only an irreducible tree-shift of finite type but also a mixing tree-shift that is chaotic in the sense of Devaney. Furthermore, the graph and labeled graph representations of tree-shifts are revealed so that the verification of irreducibility and mixing of a tree-shift is equivalent to determining the irreducibility and mixing of matrices, respectively. This extends the classical results of one-sided symbolic dynamics. \nA necessary and sufficient condition for the irreducibility and mixing of tree-shifts of finite type is demonstrated. Most important of all, the examination can be done in finite steps with an upper bound. | 關聯: | Transactions of the American Mathematical Society, Vol.369, No.12, pp.8389-8407 | 資料類型: | article | DOI: | https://doi.org/10.1090/tran/6906 |
Appears in Collections: | 期刊論文 |
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