本論文旨在研究樹子平移上拓樸熵的存在性。我首先重新用符號證明了滿矩陣[2]以及黃金分割矩陣[1]為規則下拓樸熵的存在性，近一步一般化條件，證明在階層個數符和超可加性時拓樸熵存在，並給予例子印證。

In this paper, we study the existence of the tree shift topological entropy. I rewrite the proof of Karl Petersen and Ibrahim Salama[2] and the proof of Ban and Chang[1].Then, I generalize the condition that if the length of the tree shift satisfies superadditivity, the topological entropy exist.

第一章 Introduction 1
第二章 Preliminaries 2
第三章 Main theorem 2
第四章 Acknowledgements 12
第五章 References 13

[1]Jung-Chao Ban and Chih-Hung Chang,Complexity of Shift Spaces on Semigroups, arXiv:1808.04925,2018.
[2] Karl Petersen and Ibrahim Salama,Tree Shift Complexity, Theoretical Computer Science Volume 743,Pages 64-71, 2018.
[3] Jung-Chao Ban and Chih-Hung Chang,On the topological entropy of subshifts of free semigroups,arXiv:1803.03082, 2018.
[4] Jung-Chao Ban and Chih-Hung Chang,Characterization for entropy of shifts of finite type on Cayleytrees, arXiv:1705.03138, 2017.
[5] Jung-Chao Ban and Chih-Hung Chang,Tree-Shifts : The entropy of tree-shifts of finite type, Nonlin-earity, Volume 30, Number 7, 2017.
[6] Stephen G. Simpson,Symbolic dynamics: entropy = dimension = complexity, Theory ComputSyst,Volume 743, Pages 527-543, 2017.
[7] Douglas Lind and Brain Marcus,An introduction to symbolic dynamics and coding, Cambridge uni-versity press, 1995.
[8] Manfred Denker, Christian Grillenberger, and Karl Sigmund,Ergodic Theory on Compact Spaces,Number 527 in Lecture Notes in Mathematics. Springer-Verlag, 1976.