Normal forms of symmetric Hamiltonian systems
type: Item
instance of: scholarly article
title: Normal forms of symmetric Hamiltonian systems
zbMATH Open document ID: 0809.58038
published in: Journal of Differential Equations
publication date: 1995-03-29T00:00:00Z
review text: A method of reduction of a Hamiltonian to an invariant normal form is presented in the formal category. It is proved that under certain conditions on symmetry group \(\Gamma\) of Hamiltonian its invariant normal form is \(\Gamma\)-invariant too and reduction to it can be realized via a \(\Gamma\)-equivariant contactomorphism. Conditions under which there exist a \(\Gamma\)-equivariant contactomorphism reducing a \(\Gamma\)-invariant Hamiltonian to a \(\Gamma\)-invariant Birkhoff normal form are found. It is shown that in resonance cases the Birkhoff normal forms can be simplified.
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37C80
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 635878
zbMATH Keywords: Hamiltonian
zbMATH Keywords: normal form
zbMATH Keywords: symmetry
zbMATH Keywords: Birkhoff
author: M. Zhitomirskii
reviewed by: Valeriy Yumaguzhin
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1075
OpenAlex ID: W2010176388
DOI: 10.1006/JDEQ.1994.1075
description: scientific article; zbMATH DE number 635878