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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 2017-05
上傳時間 27-May-2020 09:03:03 (UTC+8)
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.
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
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