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Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem.
・ISBN 978-1-032-26065-5 hard GB£ 187.99
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| 著者・編者 | Feldmeier, Achim, |
|---|---|
| 出版社 | (CRC Press, UK) |
| 出版年月 | 2022 |
| ページ数 | 205 pp. |
| 言語 | ENG |
| ニュース番号 | ＜A01-67687＞ |
解説
INTRODUCTION TO ARNOLD'S PROOF OF THE KOLMOGOROV-ARNOLD-MOSER THEOREM
This book provides an accessible step-by-step account of Arnold's classical proof of the Kolmogorov-Arnold-Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville-Arnold theorem for integrable systems and introduces Kneser's tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold's proof, before the second half of the book walks the reader through a detailed account of Arnold's proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals.
Features
* Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics.
* Covers all aspects of Arnold's proof, including those often left out in more general or simplifi ed presentations.
* Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).