An algorithm to generate canonical transformations: Application to normal forms
type: Item
instance of: scholarly article
title: An algorithm to generate canonical transformations: Application to normal forms
zbMATH Open document ID: 1027.70025
DOI: 10.1016/S0167-2789(02)00459-1
author: A. Haro
published in: Physica D
publication date: 2002-07-17T00:00:00Z
review text: There are two classical ways to construct symplectomorphisms (i.e. canonical transformations of mechanics): using generating functions or using Lie series. In a previous paper [Nonlinearity 12, 1299-1322 (1999; Zbl 0949.37059)] the author proposed a new one, involving the so-called primitive functions. The goal of present paper is to discuss numerical issues of this new algorithm and, much more important, to use the algorithm as a tool to study dynamical systems. As a concrete application, developed in detail and numerically implemented, is the computation of the normal form of a KAM torus for area-preserving maps. Several pictures and four appendices are included.
Mathematics Subject Classification ID: 70H15
Mathematics Subject Classification ID: 70-08
zbMATH DE Number: 1768947
zbMATH Keywords: symplectomorphisms
zbMATH Keywords: primitive functions
zbMATH Keywords: KAM torus
zbMATH Keywords: normal form
zbMATH Keywords: canonical transformations
zbMATH Keywords: area-preserving maps
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1768947