Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem
Introduction to Arnold's Proof of the Kolmogorov–Arnold–Moser Theorem
English | 2022 | ISBN: 9781003287803 | 702 pages | True PDF | 4.3 MB
English | 2022 | ISBN: 9781003287803 | 702 pages | True PDF | 4.3 MB
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 and 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.