An Introduction To Small Divisors

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dc.creatorMarmi, S.
dc.date2000-09-27
dc.date.accessioned2026-07-07T04:37:42Z
dc.date.available2026-07-07T04:37:42Z
dc.descriptionThis 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
dc.description91 pages, some copies of this booklet are still available for free, please send your request to Fabrizio Broglia, Dipartimento di Matematica, Universita' di Pisa, email broglia@dm.unipi.it. Dottorato Di Ricerca In Matematica, Universita' di Pisa, anno 2000
dc.identifierhttps://arxiv.org/abs/math/0009232
dc.identifierhttp://arxiv.org/abs/math/0009232
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60001
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subjectComplex Variables
dc.subjectSymplectic Geometry
dc.titleAn Introduction To Small Divisors
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