Dynamical Systems and Small Divisors: Lectures given at the C.I.M.E. Summer School held in Cetraro Italy, June 13-20, 1998 (Lecture Notes in Mathematics / Fondazione C.I.M.E., Firenze)

Many Problems Of Stability In The Theory Of Dynamical Systems Face The Difficulty Of Small Divisors. The Most Famous Example Is Probably Given By Kolmogorov-arnold-moser Theory In The Context Of Hamiltonian Systems, With Many Applications To Physics And Astronomy. Other Natural Small Divisor Problems Arise Considering Circle Diffeomorphisms Or Quasiperiodic Schroedinger Operators. In This Volume Hakan Eliasson, Sergei Kuksin And Jean-christophe Yoccoz Illustrate The Most Recent Developments Of This Theory Both In Finite And Infinite Dimension. A List Of Open Problems (including Some Problems Contributed By John Mather And Michel Herman) Has Been Included. Hakan Eliasson: Perturbations Of Linear Quasi-periodic System -- Sergei B. Kuksin: Kam-persistence Of Finite-gap Solutions -- Jean-christophe Yoccoz: Analytic Linearization Of Circle Diffeomorphisms -- Stefano Marmi And Jean-christophe Yoccoz: Some Open Problems Related To Small Divisors. L.h. Eliasson ... [et Al.] ; Editors, S. Marmi, J.-c. Yoccoz. Includes Bibliographical References. Also Available In An Electronic Version. Front Matter....Pages I-XIII Perturbations of linear quasi-periodic system....Pages 1-60 KAM-persistence of finite-gap solutions....Pages 61-123 Analytic linearization of circle diffeomorphisms....Pages 125-173 Some open problems related to small divisors....Pages 175-191 Back Matter....Pages 193-199