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Fixed Point of the Parabolic Renormalization Operator / by Oscar E. Lanford III, Michael Yampolsky
(SpringerBriefs in Mathematics. ISSN:21918201)
版 | 1st ed. 2014. |
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出版者 | Cham : Springer International Publishing : Imprint: Springer |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | VIII, 111 p. 15 illus., 11 illus. in color : online resource |
著者標目 | *Lanford III, Oscar E author Yampolsky, Michael author SpringerLink (Online service) |
件 名 | LCSH:Dynamical systems LCSH:Functions of complex variables LCSH:Numerical analysis FREE:Dynamical Systems FREE:Functions of a Complex Variable FREE:Numerical Analysis |
一般注記 | 1 Introduction -- 2 Local dynamics of a parabolic germ -- 3 Global theory -- 4 Numerical results -- 5 For dessert: several amusing examples -- Index This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both expertsin the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics HTTP:URL=https://doi.org/10.1007/978-3-319-11707-2 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319117072 |
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EB00228214 |
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※2017年9月4日以降