Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals
type: Item
instance of: scholarly article
title: Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals
zbMATH Open document ID: 0939.65138
DOI: 10.1023/A:1019177917586
author: J. Mikram
author: F. Zinoun
published in: Numerical Algorithms
publication date: 2000-06-19T00:00:00Z
review text: Normal forms are an important tool in the analysis of Hamiltonian systems. The article discusses their construction for systems with symmetries. The authors describe explicitly how the Hamiltonian vector field and the symmetry generators can simultaneously be brought to normal form, based on the works of \textit{G. Cicogna} and \textit{G. Gaeta} [J. Phys. A 27, 461-476 (1994; Zbl 0822.34037); ibid. A 27, 7115-7124 (1994; Zbl 0847.58065)]. Parts of the algorithm have been implemented in the computer algebra system Maple. As a concrete application a Liouville integrable Hénon-Heiles system is treated in detail.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1382968
zbMATH Keywords: normal form
zbMATH Keywords: first integral
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: symmetry
zbMATH Keywords: algorithm
zbMATH Keywords: Hénon-Heiles system
describes a project that uses: Maple
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1382968