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https://ah.lib.nccu.edu.tw/handle/140.119/139043
題名: | Verification of mixing properties in two-dimensional shifts of finite type | 作者: | 班榮超 Ban, Jung-Chao Hu, Wen-Guei Lin, Song-Sun Lin, Yin-Heng |
貢獻者: | 應數系 | 日期: | Jun-2021 | 上傳時間: | 10-Feb-2022 | 摘要: | This work introduces constructive and systematic methods for verifying the topological mixing and strong specification (or strong irreducibility) of two-dimensional shifts of finite type. First, we define transition matrices on infinite strips of width n for all n ≥ 2. To determine the primitivity of the transition matrices, we introduce the connecting operators that reduce the high-order transition matrices to lower-order transition matrices. Then, two sufficient conditions for primitivity are provided; they are invariant diagonal cycles and primitive commutative cycles of connecting operators. Then, the primitivity, corner-extendability, and crisscross-extendability are used to demonstrate the topological mixing. Finally, we show that the hole-filling condition yields the strong specification property. The application of all the above-mentioned conditions can be verified in a finite number of steps. | 關聯: | Journal of Mathematical Physics, Vol.62, No.7, pp.072703 | 資料類型: | article | DOI: | http://dx.doi.org/10.1063/5.0007365 |
Appears in Collections: | 期刊論文 |
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