An abstract KAM theorem
type: Item
instance of: scholarly article
zbMATH Open document ID: 1344.37069
publication date: 2016-04-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1308.4522
full work available at URL: 2014-014-004-005.html
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37K55
zbMATH DE Number: 6572510
zbMATH Keywords: KAM theory
zbMATH Keywords: Arnold spaces
zbMATH Keywords: perturbation theory
author: Mauricio Garay
MaRDI profile type: Publication
arXiv ID: 1308.4522
arXiv classification: math.DS
title: An abstract KAM theorem
published in: Moscow Mathematical Journal
review text: The article provides an abstract (categorical) setting for iterative processes which are used to prove normal form theorems or to solve functional equations. In general, to obtain such normal forms, one needs to prove the convergence of iterations coming from compositions of changes of local coordinates. The main theorem is formulated in terms of bounded morphisms of Arnold spaces. One important application is the proof of stability, under perturbations, of invariant tori for some Hamiltonian system (KAM theorem). Another remarkable consequence pointed out by the author is his proof of the Herman conjecture about the measure of the set of invariant tori.
reviewed by: Mário Jorge Dias Carneiro
description: scientific article; zbMATH DE number 6572510