| dc.contributor | 應數系 | |
| dc.creator (作者) | 班榮超 | |
| dc.creator (作者) | Ban, Jung-Chao | |
| dc.creator (作者) | Chang, Chih-Hung | |
| dc.date (日期) | 2017-05 | |
| dc.date.accessioned | 27-May-2020 09:03:03 (UTC+8) | - |
| dc.date.available | 27-May-2020 09:03:03 (UTC+8) | - |
| dc.date.issued (上傳時間) | 27-May-2020 09:03:03 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/129989 | - |
| dc.description.abstract (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. This 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. A 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. | |
| dc.format.extent | 248977 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.relation (關聯) | Transactions of the American Mathematical Society, Vol.369, No.12, pp.8389-8407 | |
| dc.title (題名) | Tree-shifts: Irreducibility, mixing, and the chaos of tree-shifts | |
| dc.type (資料類型) | article | |
| dc.identifier.doi (DOI) | 10.1090/tran/6906 | |
| dc.doi.uri (DOI) | https://doi.org/10.1090/tran/6906 | |
