Characterization of the generic unfolding of a weak focus
type: Item
instance of: scholarly article
title: Characterization of the generic unfolding of a weak focus
zbMATH Open document ID: 1277.34040
published in: Journal of Differential Equations
publication date: 2012-08-20T00:00:00Z
review text: The author considers analytic families of planar vector fields depending on a real parameter \(\mu\) and having a singular point at the origin with eigenvalues \(\alpha(\mu)\pm\beta(\mu)\,i\), with \(\alpha(0)=0\) and \(\beta(0)\neq0\), which are generic (\(\alpha'(0)\neq0\)) and when \(\mu=0\) have a weak focus of first order (the first Lyapunov constant is non-zero) at this point. He proves that their orbital class is determined by the conjugacy class of their associated Poincaré monodromy and vice versa. The natural approach to these questions is via complexification of time, coordinates and parameter. The used tools include quasiconformal surgery and normal form theory.
reviewed by: Armengol Gasull
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 6069298
zbMATH Keywords: weak focus
zbMATH Keywords: Poincaré monodromy
zbMATH Keywords: conjugacy class
zbMATH Keywords: quasiconformal surgery
author: W. Arriagada
MaRDI profile type: Publication
full work available at URL: j.jde.2012.06.013
OpenAlex ID: W2963683701
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DOI: 10.1016/J.JDE.2012.06.013
description: scientific article; zbMATH DE number 6069298