 00381 S. Marmi
 An Introduction To Small Divisors Problems
(639K, Postscript)
Sep 28, 00

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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. Onedimensional 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. DouadyGhys' Theorem. Continued Fractions and the Brjuno Function
5. SiegelBrjuno 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. Quasiintegrable Hamiltonian Systems
9. NashMoser's Implicit Function Theorem
10. From NashMoser's Theorem to KAM: Normal Form of Vector Fields on the
Torus
Appendices
A1. Uniformization, Distorsion and Quasiconformal Maps
A2. Continued Fractions
A3. Distributions, Hyperfunctions, Formal Series. Hypoellipticity
and Diophantine Conditions
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