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| 研究生： |
陳耿彥 Chen Keng-Yen |
|---|---|
| 論文名稱： |
Some Results on Holomorphic Mappings on C^n 複 n 維空間上的解析映射 |
| 指導教授： |
陳天進
Chen Ten-Ging |
| 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： | 2006 |
| 畢業學年度： | 91 |
| 語文別： | 英文 |
| 論文頁數： | 29 |
| 外文關鍵詞： | complex Henon map, Fatou-Bieberbach domain, automorphism of C^n |
| 相關次數： | 點閱：110 下載：30 |
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在這篇論文裡，我們將列舉一些C^n上的解析自同構，並且探討它們的基本性質。同時，我們利用解析動態方法得到一類複域解析同構於C^n。
In this thesis, we present a large class of automorphisms of C^n and study their elementary properties. Also, we use the complex dynamic method to obtain a large class of
Fatou-Bieberbach domains in C^n, n≧2.
Abstract i
中文摘要 ii
1. Introduction 1
2. The Automorphism Group of C 2
3. Some Examples of Automprphisms of C^n 5
4. A Class of n-Dimensional Complex Henon Maps 18
and Fatou-Bieberbach Domains in C^n
References 29
[1] S. Bochner and W. Martin, Several Complex Variables,
Princeton University Press, NJ, 1948.
[2] T. G. Chen, A Class of Fatou-Bieberbach Domain in C^3, Math
Sciences Research Hotline, 5(12) 2001, pp. 39-45.
[3] F. Forstneric, Holomorphic Automorphisms of C^n: A Survey.
(Proceedings 'Complex Analysis and Geometry', Ed. V.
Ancona, E. Ballico, A. Silva; pp. 173-120) Lecture Notes in
Pure and Applied Mathematics 173, New York: Marcel Dekker
(1996).
[4] S. Krantz and R. Greene, Function Theory of One Complex
Variable, John Wiley and Sons, New York, 1997.
[5] S. Krantz, Function Theory of Several Complex Variables,
2nd ed., Wadsworth, Belmont, CA, 1992.
[6] R. Michael Range, Holomorphic Functions and Integral
Representations in Several Complex Variables, Springer-
Verlag, New York, 1986.
[7] J. P. Rosay and W. Rudin, Holomorphic maps from C^n to
C^n, Trans. Amer. Math. Soc., 310(1988), pp. 47-86.