翻訳と辞書 Words near each other ・ Siege of Érsekújvár (1663) ・ Siege of Érsekújvár (1685) ・ Siege of Đông Quan ・ Siege of Ōta Castle ・ Siege of Ōtate ・ Siege of Ōtsu ・ Siege Perilous ・ Siege Perilous (Andromeda) ・ Siege Perilous (disambiguation) ・ Siege Perilous (Once Upon a Time) ・ Siege running ・ Siege tower ・ Siegel ・ Siegel + Gale ・ Siegel Center ・ Siegel disc ・ Siegel domain ・ Siegel Eisenstein series ・ Siegel G-function ・ Siegel High School ・ Siegel identity ・ Siegel modular form ・ Siegel operator ・ Siegel parabolic subgroup ・ Siegel Stores Corporation ・ Siegel Suites ・ Siegel theta series ・ Siegel upper half-space ・ Siegel zero ・ Siegel's lemma Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Siegel disc ： ウィキペディア英語版 Siegel disc Siegel disc is a connected component in the Fatou set where the dynamics is analytically conjugated to an irrational rotation. ==Description== Given a holomorphic endomorphism $f:S\backslash to\; S$ on a Riemann surface $S$ we consider the dynamical system generated by the iterates of $f$ denoted by $f^n=f\backslash circ\backslash stackrel\backslash circ\; f$. We then call the orbit $\backslash mathcal^+(z\_0)$ of $z\_0$ as the set of forward iterates of $z\_0$. We are interested in the asymptotic behavior of the orbits in $S$ (which will usually be $\backslash mathbb$, the complex plane or $\backslash mathbb=\backslash mathbb\backslash cup\backslash$, the Riemann sphere), and we call $S$ the phase plane or ''dynamical plane''. One possible asymptotic behavior for a point $z\_0$ is to be a fixed point, or in general a ''periodic point''. In this last case $f^p(z\_0)=z\_0$ where $p$ is the period and $p=1$ means $z\_0$ is a fixed point. We can then define the ''multiplier'' of the orbit as $\backslash rho=(f^p)\text{'}(z\_0)$ and this enables us to classify periodic orbits as ''attracting'' if ''superattracting'' if $|\backslash rho|=0$), ''repelling'' if $|\backslash rho|>1$ and indifferent if $\backslash rho=1$. Indifferent periodic orbits split in ''rationally indifferent'' and ''irrationally indifferent'', depending on whether $\backslash rho^n=1$ for some $n\backslash in\backslash mathbb$ or $\backslash rho^n\backslash neq1$ for all $n\backslash in\backslash mathbb$, respectively. Siegel discs are one of the possible cases of connected components in the Fatou set (the complementary set of the Julia set), according to Classification of Fatou components, and can occur around irrationally indifferent periodic points. The Fatou set is, roughly, the set of points where the iterates behave similarly to their neighbours (they form a normal family). Siegel discs correspond to points where the dynamics of $f$ is analytically conjugated to an irrational rotation of the complex disc. 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「Siegel disc」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.