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    題名: Characterization and Topological Behavior of Homomorphism Tree-Shifts
    作者: 班榮超
    Ban, Jung-Chao
    Chang, Chih-Hung
    Hu, Wen-Guei
    Lai, Guan-Yu
    貢獻者: 應數系
    關鍵詞: Tree-SFT;Sofic tree-shift;Mixing property
    日期: 2021-10
    上傳時間: 2022-02-10 14:57:57 (UTC+8)
    摘要: The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift TX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for TX. Furthermore, an equivalence between irreducibility on TA and irreducibility on XA are seen, and so is one between topologically mixing on TA and mixing property on XA, where XA is the one-sided shift space induced by the matrix A and TA is the associated tree-shift. These equivalences are consistent with the mixing properties on X or XA when viewed as a degenerate tree-shift.
    關聯: Topology and its Applications, Volume 302, 107848
    資料類型: article
    DOI 連結: https://doi.org/10.1016/j.topol.2021.107848
    DOI: 10.1016/j.topol.2021.107848
    顯示於類別:[應用數學系] 期刊論文

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