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

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.

Key features:

Applies concepts and theorems from real and complex analysis (e.g. Fourier series; 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 simplified 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).

Author: Achim Feldmeier