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An Introduction To Small Divisors

Author: S. Marmi
Url: http://babbage.sissa.it/abs/math.DS/0009232
Format: Ps, Pdf
Category: Dynamical Systems
Pages: 91
Clicks: 1125

This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small Divisors. Yoccoz's Theorems 1. Germs of Analytic Diffeomorphisms. Linearization 2. Topological Stability vs. Analytic Linearizability 3. The Quadratic Polynomial: Yoccoz's Proof of the Siegel Theorem 4. Douady-Ghys' Theorem. Continued Fractions and the Brjuno Function 5. Siegel-Brjuno Theorem, Yoccoz's Theorem. Some Open Problems 6. Small Divisors and Loss of Differentiability Part II Implicit Function Theorems and KAM Theory 7. Hamiltonian Systems and Integrable Systems 8. Quasi-Integrable Hamiltonian Systems 9. Nash-Moser's Implicit Function Theorem 10. From Nash-Moser's Theorem to KAM: Normal Form of Vector Fields on the Torus Appendices A1. Uniformization, Distorsion and Quasi-conformal maps A2. Continued Fractions A3. Distributions, Hyperfunctions. Hypoellipticity and Diophantine Conditions

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