S. Marmi
An Introduction To Small Divisors Problems
(639K, Postscript)

ABSTRACT.  The material treated in this book was brought together for a PhD
course I taught at the University of Pisa in the spring of 1999. It is
intended to be an introduction to small divisors problems.
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, Formal Series. Hypoellipticity 
and Diophantine Conditions