Structural stability of planar quasi-homogeneous vector fields
type: Item
instance of: scholarly article
title: Structural stability of planar quasi-homogeneous vector fields
zbMATH Open document ID: 1405.34047
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-09-17T00:00:00Z
review text: Let \({\mathbf t}=(t_1,t_2)\), where \(t_1\) and \(t_2\) are relatively prime nonnegative integers. Denote by \({\mathcal P}^{\mathbf t}_k\) the set of polynomials \(f\) of two variables such that \[ f(\varepsilon ^{t_1}x,\varepsilon ^{t_2}y)=\varepsilon ^{k}f(x,y). \] The authors consider the space \({\mathcal Q}^{\mathbf t}_{k}\) of planar vector fields \(F=(P,Q)\), where \[ P\in {\mathcal P}^{\mathbf t}_{k+t_1},\quad Q\in {\mathcal P}^{\mathbf t}_{k+t_2}. \] They obtain conditions on a vector field \(F\in {\mathcal Q}^{\mathbf t}_{k}\) under which \(F\) is topologically equivalent to the perturbed fields \(H=F+\varepsilon G\), where \(\varepsilon\) is a small parameter and \(G\in {\mathcal Q}^{\mathbf t}_{k}\).
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 6937849
zbMATH Keywords: structural stability
zbMATH Keywords: planar vector fields
author: Antonio Algaba
author: N. Fuentes
author: Estanislao Gamero
author: Cristóbal García
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.08.005
OpenAlex ID: W2885791219
cites work: Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems
cites work: Centers of quasi-homogeneous polynomial planar systems
cites work: The integrability problem for a class of planar systems
cites work: Integrability of two dimensional quasi-homogeneous polynomial differential systems
cites work: Q5765500
cites work: Structural Stability of Planar Hamiltonian Polynomial Vector Fields
cites work: Q4854249
cites work: Structural stability of planar homogeneous polynomial vector fields: Applications to critical points and to infinity
cites work: Structural stability of planar semi-homogeneous polynomial vector fields. Applications to critical points and to infinity
cites work: Structural stability of planar quasihomogeneous vector fields
cites work: Structural stability on two-dimensional manifolds
cites work: Structural stability and generic properties of planar polynomial vector fields
cites work: Structure and Stability of Gradient Polynomial Vector Fields
Wikidata QID: Q129396246
DOI: 10.1016/J.JMAA.2018.08.005
description: scientific article