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

Achim Feldmeier

$96.99

Paperback

Forthcoming
Pre-Order now

QTY:

English

CRC Press
26 August 2024

Applied mathematics; Plasma physics; Mathematical physics; Life sciences: general issues

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).

By: Achim Feldmeier
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 400g
ISBN: 9781032263380
ISBN 10: 1032263385
Pages: 205
Publication Date: 26 August 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Forthcoming

Chapter 1. Hamilton Theory Chapter 2. Preliminaries Chapter 3. Outline of the KAM Proof Chapter 4. Proof of the KAM Theorem Chapter 5. Analytic Lemmas Chapter 6. Geometric Lemmas Chapter 7. Convergence Lemmas Chapter 8. Arithmetic Lemmas

Author Achim Feldmeier is a professor at Universität Potsdam, Germany.