Mendeley出力
＜図書＞
Complex dynamics and renormalization
| 責任表示 | by Curtis T. McMullen |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 135 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 1994 |
| 本文言語 | 英語 |
| 大きさ | vii, 214 p. : ill. ; 24 cm |
| 概要 | Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introd...ction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps. Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6822669 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図1F 開架 | 421.5/Ma 22 | 1994 |
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068252195000612 |
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理系図3F 数理独自 | MACM/60/1 | 1994 |
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068222194006181 |
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書誌詳細
| 一般注記 | Includes bibliography (p. 207-212) and index |
|---|---|
| 著者標目 | *McMullen, Curtis Tracy |
| 件 名 | LCSH:Renormalization LCSH:Polynomials LCSH:Dynamics LCSH:Mathematical physics |
| 分 類 | NDC8:421.5 LCC:QC20.7.R43 DC20:530.1/43/0151 |
| 書誌ID | 1000034987 |
| ISBN | 0691029822 |
| NCID | BA24013736 |
| 巻冊次 | : cloth ; ISBN:0691029822 ; PRICE:$49.50 : pbk ; ISBN:0691029814 ; PRICE:$22.50 |
| 登録日 | 2009.09.10 |
| 更新日 | 2009.09.17 |