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研究生： 吳昱瑩
Yu-Ying Wu
論文名稱： On the Existence of the Stem Entropy on Markov-Cayley tree
指導教授： 許正雄
Cheng-Hsiung Hsu
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2021
畢業學年度： 109
語文別： 中文
論文頁數： 33
中文關鍵詞： 符號動態空間 、拓樸熵 、莖熵
外文關鍵詞： shift spaces, topological entropy, stem entropy
相關次數： 點閱：13  下載：0 
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    • 這篇論文當中，我們定義馬可夫－凱利樹在其分支的熵，並證明其極限
    之存在性。

    In this thesis, we define the stem entropy, as well as prove that the stem entropy of a Markov-Cayley tree shift exists in limit.

    1 Introduction 1 2 Stem Entropy on Markov-Cayley tree 4 2.1 Preliminaries . ................................. 4 2.2 The Existence of Stem Entropy . ....................... 6 2.3 Proof of the Theorem . ............................. 7 3 A Discussion of Intermediate Entropy 18 Reference 25

    [1]Hadamard, Les surfaces à courbures opposées et leurs lignes géodésiques. Journal de Mathématiques Pures et Appliquées, Vol 4, 27-74, 1898.
    [2]D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, 1995.
    [3]N. Aubrun and M. P. Béal, Decidability of Conjugacy of Tree-Shifts of Finite Type. Lecture Notes in Computer Science, Vol 5555, 132-143, 2009.
    [4]K. Petersen and I. Salama, Tree shift topological entropy. Theoretical Computer Science, Vol 743, 64-71, 2018.
    [5]K. Petersen and I. Salama, Entropy on regular trees, Discret. Contin. Dyn. Syst. Ser. A 40 (2020), no. 7, 4453–4477.
    [6]Y. Shen, S. Tan, A. Sordoni and A. Courville, Ordered Neurons: Integrating Tree Structures into Recurrent Neural Networks. In International Conference on Learning Representations, 2019.
    [7]J.-C. Ban and C.-H. Chang, Tree-shifts: the entropy of tree-shifts of finite type. Nonlinearity, 2785-2804, 2017.
    [8] J.-C. Ban and C.-H. Chang,Complexity of neural networks on Fibonacci-Cayley tree. Journal of Algebra Combinatorics, 105-122, 2019.
    [9]J.-C. Ban, C.-H. Chang, Y.-Y. Wu, and Y.-L. Wu, Stem and Topological Entropy on Cayley Trees. Manuscript submitted for publication.

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