INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREMThis 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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This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem.
Chapter 1. Hamilton TheoryChapter 2. PreliminariesChapter 3. Outline of the KAM ProofChapter 4. Proof of the KAM TheoremChapter 5. Analytic LemmasChapter 6. Geometric LemmasChapter 7. Convergence LemmasChapter 8. Arithmetic Lemmas
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Produktdetaljer
ISBN
9781032263380
Publisert
2024-08-26
Utgiver
Vendor
CRC Press
Vekt
400 gr
Høyde
234 mm
Bredde
156 mm
Aldersnivå
U, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
205
Forfatter
Biographical note
Author
Achim Feldmeier is a professor at Universität Potsdam, Germany.