臺灣博碩士論文加值系統

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.