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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 Complex quadratic polynomial ： ウィキペディア英語版 Complex quadratic polynomial A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers. ==Forms== When the quadratic polynomial has only one variable (univariate), one can distinguish its 4 main forms: * The general form: $f(x)\; =\; a\_2\; x^2\; +\; a\_1\; x\; +\; a\_0\; \backslash qquad\; \backslash ,$ where $\backslash qquad\; a\_2\; \backslash ne\; 0$ * The factored form used for logistic map $f\_r(x)\; =\; r\; x\; (\; 1-x\; )\; \backslash ,$ * $f\_(x)\; =\; x^2\; +\; e^\; x\; \backslash ,$ which has an indifferent fixed point with multiplier $\backslash lambda\; =\; e^\; \backslash ,$ at the origin〔(Michael Yampolsky, Saeed Zakeri : Mating Siegel quadratic polynomials. )〕 * The monic and centered form, $f\_c(x)\; =\; x^2\; +c\backslash ,$ The monic and centered form has the following properties: * It is the simplest form of a nonlinear function with one coefficient (parameter), * It is an unicritical polynomial, i.e. it has one critical point, * It is a centered polynomial (the sum of its critical points is zero),〔Bodil Branner: Holomorphic dynamical systems in the complex plane. Mat-Report No 1996-42. Technical University of Denmark〕 * It can be postcritically finite, i.e. If the orbit of the critical point is finite. It is when critical point is periodic or preperiodic.〔(Alfredo Poirier : On Post Critically Finite Polynomials Part One: Critical Portraits )〕 * It is a unimodal function, * It is a rational function, * It is an entire function. 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「Complex quadratic polynomial」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.