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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/149595
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/149595


    Title: 關於二元樹上一階馬可夫平移之條型熵研究
    Strip entropy approximation for 1-step Markov shifts of the binary tree
    Authors: 陳芊瑜
    Chen, Chien-Yu
    Contributors: 班榮超
    Ban, Jung-Chao
    陳芊瑜
    Chen, Chien-Yu
    Keywords: 條型熵
    拓樸熵
    高次區塊平移
    黃金平均
    strip entropy
    topological entropy
    higher block shift
    golden-mean
    Date: 2024
    Issue Date: 2024-02-01 11:25:39 (UTC+8)
    Abstract: Petersen 和Salama(cf. [1], [2]) 證明d 維樹平移中拓樸熵的存在性, 之後獨創條型法取最左邊的分支作為基礎, 估算黃金平均規則在d 維樹上的條型熵, 並發現條型熵會收斂至拓樸熵的性質。本篇論文運用條型法, 將黃金平
    均平移轉換為其高次區塊平移, 去計算在二元樹上沿著任意路徑的條型熵,
    並證明條型熵依舊收斂至拓樸熵。
    Petersen and Salama(cf. [1], [2]) demonstrated the existence of topological
    entropy in d-dimensional tree-shift. Subsequently, strip method was innovatively
    developed. They take the leftmost branch as the base to estimate the strip entropy
    of the golden-mean rule on d-dimensional tree. It was observed that the strip
    entropy converges to the topological entropy. This paper applies the strip method.
    It transforms the golden-mean shift into its higher block shift. The purpose is to
    calculate the strip entropy along arbitrary path on binary tree. It is demonstrated
    that the strip entropy still converges to the topological entropy.
    Reference: [1] Karl Petersen and Ibrahim Salama. Tree shift topological entropy. Theoretical Computer
    Science, 743:64–71, 2018.
    [2] Karl Petersen and Ibrahim Salama. Entropy on regular trees. Discrete & Continuous
    Dynamical Systems, 40(7):4453, 2020.
    [3] Douglas Lind and Brian Marcus. An introduction to symbolic dynamics and coding.
    Cambridge university press, 2021.
    [4] Jung-Chao Ban and Chih-Hung Chang. Tree-shifts: The entropy of tree-shifts of finite type.
    Nonlinearity, 30(7):2785, 2017.
    [5] Wei-Lin Lin. On the strip entropy of the golden-mean tree shift. Master’s thesis, National
    Chengchi University, 2021.
    [6] Jung-Chao Ban, Guan-Yu Lai, and Cheng-Yu Tsai. The strip entropy approximation of
    markov shifts on trees. arXiv preprint arXiv:2309.00309, 2023.
    [7] Jung-Chao Ban and Chih-Hung Chang. Characterization for entropy of shifts of finite type
    on cayley trees. Journal of Statistical Mechanics: Theory and Experiment, 2020(7):073412,
    2020.
    Description: 碩士
    國立政治大學
    應用數學系
    110751017
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0110751017
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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