Geometry of Continued Fractions
Karpenkov, Oleg N.
- 出版商: Springer
- 出版日期: 2023-05-30
- 售價: $2,370
- 貴賓價: 9.5 折 $2,252
- 語言: 英文
- 頁數: 451
- 裝訂: Quality Paper - also called trade paper
- ISBN: 366265279X
- ISBN-13: 9783662652794
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商品描述
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.
Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics.
The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
商品描述(中文翻譯)
這本書介紹了一種新的幾何視角的連分數。它涵蓋了多個應用領域，如丟番圖逼近、代數數論和拓撲幾何學等。第二版現在還包括了高斯約化理論的幾何方法、整數正多邊形的分類以及一些新的主題。
傳統上，連分數是數論的一個主題，它出現在動力系統、代數幾何、拓撲學，甚至天體力學中。計算幾何學的興起使得對多維連分數的廣義化產生了新的興趣。許多經典定理已經擴展到多維情況，為數學的各個領域的現象提供了新的視角。
讀者將在這本書中找到關於多維連分數幾何理論的最新進展概述，並附有當前的開放問題。在可能的情況下，我們用圖例和例子來說明幾何構造。每章都有對本科或研究生課程有用的練習題。
作者簡介
Oleg Karpenkov is a mathematician at the University of Liverpool (UK), working in the general area of discrete geometry and its applications. More specifically, his research interests include geometry of numbers, discrete and semi-discrete differential geometry and self-stressed configurations of graphs. Oleg has completed his Ph.D. at Moscow State University under the supervision of Vladimir Arnold in 2005. Further he held several postdoctoral positions in Paris (Fellowship of the Mairie de Paris), Leiden, and Graz (Lise Meitner Fellowship) before arriving in Liverpool in 2012. In 2013 he published a book "Geometry of Continued Fractions" (its extended second edition will be available soon). Currently his Erdos number is 3.
作者簡介(中文翻譯)
Oleg Karpenkov是英國利物浦大學的數學家，他的研究領域是離散幾何學及其應用。更具體地說，他的研究興趣包括數字幾何學、離散和半離散微分幾何學以及圖形的自應力配置。Oleg於2005年在莫斯科國立大學在Vladimir Arnold的指導下完成了他的博士學位。之後，他在巴黎（巴黎市政府獎學金）、萊頓和格拉茨（Lise Meitner獎學金）擔任了幾個博士後職位，並於2012年來到利物浦。2013年，他出版了一本名為《連分數的幾何學》的書（擴展第二版即將推出）。目前，他的Erdos數為3。
