Description
Taylor and Francis Ltd Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem 1st Edition 2022 Hardbound by Feldmeier, Achim
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). Chapter 1. Hamilton TheoryChapter 2. PreliminariesChapter 3. Outline of the KAM ProofChapter 4. Proof of the KAM TheoremChapter 5. Analytic LemmasChapter 6. Geometric LemmasChapter 7. Convergence LemmasChapter 8. Arithmetic Lemmas