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| 研究生： |
陳芊瑜 Chen, Chien-Yu |
|---|---|
| 論文名稱： |
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 |
| 指導教授： |
班榮超
Ban, Jung-Chao |
| 口試委員: |
曾睿彬
Tseng, Jui-Pin 張志鴻 Chang, Chih-Hung |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 英文 |
| 論文頁數： | 15 |
| 中文關鍵詞： | 條型熵 、拓樸熵 、高次區塊平移 、黃金平均 |
| 外文關鍵詞： | strip entropy, topological entropy, higher block shift, golden-mean |
| 相關次數： | 點閱：33 下載：17 |
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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.
1 Introduction 1
2 Strip entropy approximation 6
2.1 Preliminary 6
2.2 Main results 8
3 Conclusion 14
References 15
[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.
