Structural stability of planar quasihomogeneous vector fields
type: Item
instance of: scholarly article
title: Structural stability of planar quasihomogeneous vector fields
zbMATH Open document ID: 1318.34076
author: Yulin Zhao
author: Regilene Oliveira
published in: Qualitative Theory of Dynamical Systems
publication date: 2015-01-27T00:00:00Z
review text: The authors consider the space \(H_{pqm}\) of planar vector fields of the form \((P,Q)\), where \(p,q,m\) are positive integers, \[ P=\sum a_{ij}x^iy^j,\quad Q=\sum b_{ij}x^iy^j, \] and the sums are taken over \((i,j)\) such that \(pi+qj=p-1+m\) and \(pi+qj=q-1+m\), respectively. They characterize the set \(\Omega_{pqm}\) of structurally stable fields in \(H_{pqm}\) (with respect to the coefficient topology), determine the number of topological equivalence classes in \(\Omega_{pqm}\), and prove an analog of the Grobman--Hartman theorem at the origin for a class of vector fields starting with a term \(X\in\Omega_{pqm}\).
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 6391414
zbMATH Keywords: structural stability
zbMATH Keywords: quasihomogeneous vector fields
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
full work available at URL: s12346-013-0105-5
OpenAlex ID: W1984557961
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DOI: 10.1007/S12346-013-0105-5
description: scientific article; zbMATH DE number 6391414