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

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).