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| Full Title | Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem 1st Edition |
|---|---|
| Author(s) | Achim Feldmeier |
| Edition | 1st Edition |
| ISBN | 9781000610000, 9781032263380, 9781032260655, 9781003287803, 9781000609974 |
| Publisher | CRC Press |
| Format | PDF and EPUB |
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).
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