Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/129989
DC Field | Value | Language |
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dc.contributor | 應數系 | |
dc.creator | 班榮超 | |
dc.creator | Ban, Jung-Chao | |
dc.creator | Chang, Chih-Hung | |
dc.date | 2017-05 | |
dc.date.accessioned | 2020-05-27T01:03:03Z | - |
dc.date.available | 2020-05-27T01:03:03Z | - |
dc.date.issued | 2020-05-27T01:03:03Z | - |
dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/129989 | - |
dc.description.abstract | 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. | |
dc.format.extent | 248977 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.relation | Transactions of the American Mathematical Society, Vol.369, No.12, pp.8389-8407 | |
dc.title | Tree-shifts: Irreducibility, mixing, and the chaos of tree-shifts | |
dc.type | article | |
dc.identifier.doi | 10.1090/tran/6906 | |
dc.doi.uri | https://doi.org/10.1090/tran/6906 | |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.grantfulltext | restricted | - |
item.cerifentitytype | Publications | - |
Appears in Collections: | 期刊論文 |
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