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
|Author Institutional Affiliation|
Dipartimento di Matematica e Informatica
Università di Udine (Italy)
|Tutorial Level||Advanced Tutorial|