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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 Escaping set ： ウィキペディア英語版 Escaping set In mathematics, and particularly complex dynamics, the escaping set of an entire function ƒ consists of all points that tend to infinity under the repeated application of ƒ.〔 〕 That is, a complex number $z\_0\backslash in\backslash mathbb$ belongs to the escaping set if and only if the sequence defined by $z\_\; :=\; f(z\_n)$ converges to infinity as $n$ gets large. The escaping set of $f$ is denoted by $I(f)$.〔 For example, for $f(z)=e^z$, the origin belongs to the escaping set, since the sequence :$0,1,e,e^e,e^,\backslash dots$ tends to infinity. == History == The iteration of transcendental entire functions was first studied by Pierre Fatou in 1926〔 〕 The escaping set occurs implicitly in his study of the explicit entire functions $f(z)=z+1+\backslash exp(-z)$ and $f(z)=c\backslash sin(z)$. The first study of the escaping set for a general transcendental entire function is due to Alexandre Eremenko.〔 〕 He conjectured that every connected component of the escaping set of a transcendental entire function is unbounded. This has become known as ''Eremenko's Conjecture''.〔 There are many partial results on this problem but as of 2013 the conjecture is still open. Eremenko also asked whether every escaping point can be connected to infinity by a curve in the escaping set; it was later shown that this is not the case. Indeed, there exist entire functions whose escaping sets do not contain any curves at all.〔 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「Escaping set」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.