Introduction to Arnold's Proof of the Kolmogorov-Arnold-Moser Theorem (eBook)

Achim Feldmeier (Autor)

eBook Download: PDF

2022
217 Seiten
CRC Press (Verlag)
978-1-000-60997-4 (ISBN)

Infos

INTRODUCTION TO ARNOLD'S PROOF OF THE KOLMOGOROV-ARNOLD-MOSER THEOREMThis 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).

Produkt-Details

• Erscheint lt. Verlag: 8.7.2022
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Plasmaphysik
• ISBN-10: 1-000-60997-9 / 1000609979
• ISBN-13: 978-1-000-60997-4 / 9781000609974