Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem

<p>INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM</p><p>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.</p><p><strong>Features</strong></p><p>• 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.</p><p>• Covers all aspects of Arnold’s proof including those often left out in more general or simplifi ed presentations.</p><p>• 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). </p>