Dynamical Systems and Small Divisors: Lectures given at the C.I.M.E. Summer School held in Cetraro Italy, June 13-20, 1998 / Edition 1

by Hakan Eliasson, Stefano Marmi, Sergei Kuksin, Jean-Christophe Yoccoz

Overview

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.

Product Details

ISBN-13:	9783540437260
Publisher:	Springer Berlin Heidelberg
Publication date:	08/15/2002
Series:	Lecture Notes in Mathematics , #1784
Edition description:	2002
Pages:	202
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Perturbations of linear quasi-periodic system.- KAM-persistence of finite-gap solutions.- Analytic linearization of circle diffeomorphisms.- Some open problems related to small divisors.