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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Periodic points of complex quadratic mappings ： ウィキペディア英語版 Periodic points of complex quadratic mappings This article describes periodic points of some complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a quadratic map is one that involves the previous value raised to the powers one and two; and a complex map is one in which the variable and the parameters are complex numbers. A periodic point of a map is a value of the variable that occurs repeatedly after intervals of a fixed length. These periodic points play a role in the theories of Fatou and Julia sets. ==Definitions== Let :$f\_c(z)=z^2+c\backslash ,$ be the complex quadric mapping, where $z$ and $c$ are complex-valued. Notationally, $\backslash \; f^\; \_c\; (z)$ is the $\backslash \; k$ -fold composition of $f\; \_c\backslash ,$ with itself—that is, the value after the ''k''-th iteration of function $f\; \_c.\backslash ,$ Thus :$\backslash \; f^\; \_c\; (z)\; =\; f\_c(f^\; \_c\; (z)).$ Periodic points of a complex quadratic mapping of period $\backslash \; p$ are points $\backslash \; z$ of the dynamical plane such that :$f^\; \_c\; (z)\; =\; z,$ where $\backslash \; p$ is the smallest positive integer for which the equation holds at that ''z''. We can introduce a new function: :$\backslash \; F\_p(z,f)\; =\; f^\; \_c\; (z)\; -\; z,$ so periodic points are zeros of function $\backslash \; F\_p(z,f)$: points ''z'' satisfying :$F\_p(z,f)\; =\; 0,$ which is a polynomial of degree $2^p.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Periodic points of complex quadratic mappings」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.