KAM theory in configuration space
type: Item
instance of: scholarly article
title: KAM theory in configuration space
zbMATH Open document ID: 0682.58014
DOI: 10.1007/BF02564665
author: Dietmar A. Salamon
author: Eduard Zehnder
published in: Commentarii Mathematici Helvetici
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140144
review text: A Hamiltonian system is considered in the 2n-dimensional space and the Hamiltonian is supposed to be periodic in the first n coordinates, i.e. the system is defined on \(T^ n\times R^ n\) where \(T^ n\) is the n- dimensional torus. The problem is transformed into a variational problem whose Euler-Lagrange equation gives rise to a nonlinear partial differential equation. The latter's solution is a diffeomorphism on \(T^ n\). This solution gives rise to invariant tori of prescribed periods. The proofs are intricate. The existence proof is based upon a Newton type iteration technique. For given prescribed periods the uniqueness of the corresponding invariant torus is also proved.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 4117495
zbMATH Keywords: variational problem
zbMATH Keywords: nonlinear partial differential equation
zbMATH Keywords: diffeomorphism
zbMATH Keywords: iteration technique
zbMATH Keywords: invariant torus
reviewed by: M. Farkas
MaRDI profile type: Publication
OpenAlex ID: W2063897313
description: scientific article; zbMATH DE number 4117495