Existence of invariant tori for certain weakly reversible mappings
type: Item
instance of: scholarly article
title: Existence of invariant tori for certain weakly reversible mappings
zbMATH Open document ID: 1030.37042
author: Bao She Wei
publication date: 2004-02-09T00:00:00Z
review text: The author considers the mapping \({\mathcal M}\) close to an integrable one \(x_1=x+h(y)+f(x,y)\), \(y_1=y+g(x,y)\) and close to an involution \(x_1=-x+p(x,y)\), \(y_1=y+q(x,y)\) where \((x,y)\in T^m\times O(\Omega)\), \(\Omega\in \mathbb{R}^n\) is the closure of a connected bounded open domain and \(O(\Omega)\) is some neighborhood of \(\Omega,f(x,y),g(x,y)\) and \(p(x,y),q(x,y)\) are perturbations. The mapping \({\mathcal M}\) is weakly reversible with respect to the mapping \({\mathcal G}\), i.e. \({\mathcal M}{\mathcal G}{\mathcal M}={\mathcal G}\). Under some weak non-degeneracy condition a uniform KAM iteration is constructed for the proof of the existence of a Cantor family of \(m\)-tori invariant under the reversible mapping \({\mathcal M}\) and the reversing mapping \({\mathcal G}\).
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 70K43
zbMATH DE Number: 1921161
zbMATH Keywords: weakly reversible mappings
zbMATH Keywords: weak non-degeneracy condition
zbMATH Keywords: invariant tori
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: s10114-002-0180-z
OpenAlex ID: W2065221411
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DOI: 10.1007/S10114-002-0180-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1921161