vbid/9781000610000

Description

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).Typham this is the title: Introduction to Arnold�s Proof of the Kolmogorov�Arnold�Moser Theorem 1st Edition