Local behavior of planar analytic vector fields via integrability
type: Item
instance of: scholarly article
title: Local behavior of planar analytic vector fields via integrability
zbMATH Open document ID: 1237.34035
author: Antoni Ferragut
author: M. J. Álvarez
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-24T00:00:00Z
review text: A method to study the behaviour of trajectories near a singular point in planar analytic systems of the form \[ \dot{x}=P(x,y),\;\;\dot{y}=Q(x,y) \] is presented. It can be applied provided the system has a first integral which is a quotient of analytic functions. In particular, the method can be applied to vector fields with a rational first integral. Examples illustrate the method.
reviewed by: Gheorghe Tigan
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 5962606
zbMATH Keywords: planar analytic vector field
zbMATH Keywords: generalized rational first integral
zbMATH Keywords: blow-up
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.06.062
OpenAlex ID: W2087957477
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DOI: 10.1016/J.JMAA.2011.06.062
description: scientific article; zbMATH DE number 5962606