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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:122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.

    Contents 1 Introduction 1 2 Extenal Rays 3 3 Rotation Numbers 9 4 Critical Portraits 14 5 Fixed Point Portraits 17 6 Classification of Degree 3 Fixed Point Portraits 20

    References
    [AFB] Alan F. Beardon, Iteration of Rational Functions, Springer (1991).
    [BFH] B. Bielefeld, Y. Fisher, J. H. Hubbard, The dynamic of a kinetic activatorinhibitor
    system, Journal of the American Mathematical Society 5 (1992),
    721–762.
    [CR] Clark Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and
    Chaos, CRC, 1995, 49-52.
    [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.

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