Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem
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Book Overview
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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