多項式的臨界點圖樣和固定點圖樣

Abstract

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.