Mendeley出力
＜図書＞
The geometry of fractal sets
| 責任表示 | K.J. Falconer |
|---|---|
| シリーズ | Cambridge tracts in mathematics ; 85 |
| データ種別 | 図書 |
| 出版情報 | Cambridge [Cambridgeshire] ; New York : Cambridge University Press , 1985 |
| 本文言語 | 英語 |
| 大きさ | xiv, 162 p. : ill. ; 24 cm |
| 概要 | This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of...such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods. This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/7015887 |
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 | 414/F 13 | 1985 |
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068252190010998 |
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理系図3F 数理独自 | FALC/20/1 | 1992 |
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068222193002953 |
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理系図3F 数理独自 | FALC/20/1A | 1992 |
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068222193003016 |
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理 物理 統計物理 | 20/F/16 |
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068222186004667 |
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数理 雑誌室 | SER/CTM/K85A | 1985 |
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068252184011372 |
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数理 雑誌室 | SER/CTM/K85 | 1985 |
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068252186007593 |
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書誌詳細
| 一般注記 | Bibliography: p. [150]-160 Includes index |
|---|---|
| 著者標目 | *Falconer, K. J., 1952- |
| 件 名 | LCSH:Fractals LCSH:Geometric measure theory NDLSH:変分法 |
| 分 類 | LCC:QA248 DC19:515/.64 NDC8:413.9 NDC8:414 |
| 書誌ID | 1000028511 |
| ISBN | 0521256941 |
| NCID | BA00234887 |
| 巻冊次 | : hard covers ; ISBN:0521256941 : paperback ; ISBN:0521337054 |
| 登録日 | 2009.09.10 |
| 更新日 | 2009.09.17 |