Dynamical Systems and Small Divisors

Lectures given at the C.I.M.E. Summer School held in Cetraro Italy, June 13-20, 1998
1. Auflage 2002
ISBN: 978-3-540-43726-0
Verlag: Springer

Buch, Englisch, 202 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 345 g

Reihe: C.I.M.E. Foundation Subseries

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.

Zielgruppe

Research

Autoren/Hrsg.

Eliasson, Hakan

Kuksin, Sergei

Marmi, Stefano

Yoccoz, Jean-Christophe

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

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