Introduction to Arnolds Proof of the KolmogorovArnoldMoser Theorem

INTRODUCTION TO ARNOLDS PROOF OF THE KOLMOGOROVARNOLDMOSER THEOREM This book provides an accessible step-by-step account of Arnolds classical proof of the KolmogorovArnoldMoser (KAM) Theorem. It begins with a general background of the theorem, proves the famous LiouvilleArnold theorem for integrable systems and introduces Knesers tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnolds proof, before the second half of the book walks the reader through a detailed account of Arnolds 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 Arnolds 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).