Global characterization of the normal form for a vector field near a closed orbit
type: Item
instance of: scholarly article
title: Global characterization of the normal form for a vector field near a closed orbit
zbMATH Open document ID: 0656.58028
DOI: 10.1016/0022-0396(88)90063-0
published in: Journal of Differential Equations
publication date: 1988-01-01T00:00:00Z
review text: A simple global characterization of normal forms for vector fields near a singularity was given recently by \textit{C. Elphick}, \textit{E. Tirapegui}, \textit{M. Brachet}, \textit{P. Coullet}, and the author [Physica D 29, 95-127 (1987; Zbl 0633.58020)]. In this paper, the author derives a natural generalization of this global characterization for vector fields near a closed orbit. The global characterization presented here separates the time law for the phase along the closed curve and the transverse dynamics in terms of this phase. This is expressed by a natural extension of the characterization obtained in the autonomous case, again in a constructive way.
reviewed by: Ding Tongren
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 4071973
zbMATH Keywords: normal forms
zbMATH Keywords: closed orbit
zbMATH Keywords: global characterization
zbMATH Keywords: transverse dynamics
author: Gérard Iooss
MaRDI profile type: Publication
full work available at URL: 0022-0396(88)90063-0
OpenAlex ID: W2070586383
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description: scientific article; zbMATH DE number 4071973