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

di Achim Feldmeier (Autore)

Taylor & Francis Ltd, 2022

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).

• Autore: Achim Feldmeier
• Editore: Taylor & Francis Ltd
• Anno: 2022
• Rilegatura: Hardback
• Pagine: 205 p.
• Dimensioni: 234 x 156 mm
• Peso: 426 gr.
• EAN: 9781032260655

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