Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem
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- ISBN 9781032260655
- Weight: 426g
- Dimensions: 156 x 234mm
- Publication Date: 08 Jul 2022
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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).
Author
Achim Feldmeier is a professor at Universität Potsdam, Germany.
