A characterization of isochronous centres in terms of symmetries.
type: Item
instance of: scholarly article
title: A characterization of isochronous centres in terms of symmetries.
zbMATH Open document ID: 1087.34010
DOI: 10.4171/RMI/386
author: Armengol Gasull
author: Antoni Guillamon
author: Emilio Freire Macías
published in: Revista Matemática Iberoamericana
publication date: 2004-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/39635
review text: Summary: We present a description of isochronous centres of planar vector fields \(X\) by means of their groups of symmetries. More precisely, given a normalizer \(U\) of \(X\) (i.e., \([X,U]=\mu X\),~where \(\mu\) is a scalar function), we provide a necessary and sufficient isochronicity condition based on \(\mu\). This criterion extends the result of Sabatini and Villarini that establishes the equivalence between isochronicity and the existence of commutators (\([X,U]= 0\)). We put also special emphasis on the mechanical aspects of isochronicity; this point of view forces a deeper insight into the potential and quadratic-like Hamiltonian systems. For these families, we provide new ways to find isochronous centres, alternative to those already known from the literature.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 37J45
zbMATH DE Number: 2104144
zbMATH Keywords: quadratic-like Hamiltonian systems
zbMATH Keywords: isochronous centres
MaRDI profile type: Publication
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OpenAlex ID: W1994645537
description: scientific article; zbMATH DE number 2104144