研究生: |
楊昌宸 Chang-chen Yang |
---|---|
論文名稱: |
多項式的臨界點圖樣和固定點圖樣 Critical Portraits and Fixed Point Portraits for Polynomial Maps |
指導教授: |
林延輯
Lin, Yen-Chi |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2009 |
畢業學年度: | 97 |
語文別: | 中文 |
論文頁數: | 25 |
中文關鍵詞: | 複變動態系統 、多項式函數疊代 、旋轉數 、固定點圖樣 |
英文關鍵詞: | Complex Dynamics, iteration for polynomial maps, rotation number, fixed point portraits |
論文種類: | 學術論文 |
相關次數: | 點閱:138 下載:3 |
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根據Goldberg-Milnor的文章[GM],具有某種性質的準固定點圖樣P可以產生數個臨界點圖樣Θ。由費雪主要定理存在唯一的首么多項式f其臨界點圖樣以及固定點圖樣分別是Θ和P。最後我們完成三次臨界點圖樣的分類。
From the work of Goldberg-Milnor [GM], a candidate of fixed point portraits P under specific conditions can generate critical portraits Θ, though there are still many possible choices for Θ. Using Fisher's main Theorem, there is a unique monic polynomial f which is critically periodic and realizes one of the critical portrait Θ and in turn realizes the fixed point portrait P. At the end we pay our attention to the case of critical portraits of degree 3 and classify them.
References
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[CR] Clark Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and
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[D] Robert L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison
Wesley 2nd Ed. (1991).
[G] Lisa R. Goldberg, Fixed points of polynomial maps. Part I. Rotation subsets
of the circles, Ann. scient. E c. Norm. Sup. 4 (1992), 679-685.
[GM] Lisa R. Goldberg and John Milnor, Fixed points of polynomial maps. Part II.
Fixed point portraits, Ann. scient. Ec. Norm. Sup. 4 (1993), 51-98.
[J] John Milnor, Dynamics in One Complex Variable, Princeton University Press
3rd Ed. (2006).
[P] Alfredo Poirier, On Post Critically Finite Polynomials. Part One: Critical Portraits,
(1993), 11-15.