Mendeley出力
＜図書＞
Outer billiards on kites
| 責任表示 | Richard Evan Schwartz |
|---|---|
| シリーズ | Annals of mathematics studies ; 171 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 2009 |
| 本文言語 | 英語 |
| 大きさ | xii, 306 p. : ill. ; 24 cm |
| 概要 | "Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B.H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial...mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks whether or not one can have an outer billiards system with an unbounded orbit. The Moser-Neumann question is an idealized version of the question of whether, because of small disturbances in its orbit, the Earth can break out of its orbit and fly away from the Sun. In Outer Billiards on Kites, Richard Schwartz presents his affirmative solution to the Moser-Neumann problem. He shows that an outer billiards system can have an unbounded orbit when defined relative to any irrational kite. A kite is a quadrilateral having a diagonal that is a line of bilateral symmetry. The kite is irrational if the other diagonal divides the quadrilateral into two triangles whose areas are not rationally related. In addition to solving the basic problem, Schwartz relates outer billiards on kites to such topics as Diophantine approximation, the modular group, self-similar sets, polytope exchange maps, profinite completions of the integers, and solenoids--connections that together allow for a fairly complete analysis of the dynamical system."--Publisher website.続きを見る |
| 目次 | Introduction The arithmetic graph The hexagrid theorem Period copying Proof of the erratic orbits theorem The master picture theorem The pinwheel lemma The torus lemma The strip functions Proof of the master picture theorem Proof of the embedding theorem Extension and symmetry Proof of hexagrid theorem I The barrier theorem Proof of hexagrid theorem II Proof of the intersection lemma Diophantine approximation The diophantine lemma The decomposition theorem Existence of strong sequences Structure of the inferior and superior sequences The comet theorem Dynamical consequences Geometric consequences Proof of the copy theorem Pivot arcs in the even case Proof of the pivot theorem Proof of the period theorem Hovering components Proof of the low vertex theorem Structure of periodic points Self-similarity General orbits on kites General quadrilaterals.続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6830995 |
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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: cloth | 理系図3F 数理独自 | SCHW/95/2 | 2009 |
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023212009005187 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. [303]-304) and index |
|---|---|
| 著者標目 | *Schwartz, Richard Evan |
| 件 名 | LCSH:Hyperbolic spaces LCSH:Singularities (Mathematics) LCSH:Transformations (Mathematics) LCSH:Geometry, Plane |
| 分 類 | LCC:QA685 DC22:516.9 |
| 書誌ID | 1001406936 |
| ISBN | 9780691142487 |
| NCID | BA91723671 |
| 巻冊次 | : cloth ; ISBN:9780691142487 : pbk ; ISBN:9780691142494 |
| 登録日 | 2009.11.24 |
| 更新日 | 2009.11.24 |