Reduction of Poincaré normal forms
type: Item
instance of: scholarly article
title: Reduction of Poincaré normal forms
zbMATH Open document ID: 0890.34031
DOI: 10.1023/A:1007341428540
author: Giuseppe Gaeta
published in: Letters in Mathematical Physics
publication date: 1998-06-29T00:00:00Z
review text: The Poincaré algorithm for reducing systems of ordinary differential equations to normal forms (near an equilibrium point) is based on considering near identity transformation of coordinates, generated by homogeneous polynomial functions, \(h_k^j\), which are chosen in such a way that nonresonant terms of the corresponding terms are eliminated. Here the same problem is studied by considering the properties of Poincaré transformations and explicit higher-order effects. Here a possibly non-unique but easily computable expression is preferable. As in the original Poincaré theory, considerations are formal in the sense that the convergence of power series used is not discussed. To help understanding the algorithm developed an example is considered.
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 1083200
zbMATH Keywords: Poincaré normal forms
zbMATH Keywords: nonlinear dynamic
zbMATH Keywords: Poincaré algorithm
zbMATH Keywords: Lie transformation
zbMATH Keywords: Poincaré transformations
reviewed by: Mahadeb Dutta
MaRDI profile type: Publication
full work available at URL: a:1007341428540
OpenAlex ID: W2914808402
description: scientific article; zbMATH DE number 1083200