Local behavior of planar analytic vector fields via integrability

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Title:	Local behavior of planar analytic vector fields via integrability
Author:	Ferragut Amengual, Antoni Manel; Álvarez, María Jesús
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Abstract:	We present an algorithm to study the local behavior of singular points of planar analytic vector fields having a first integral which is a quotient of analytic functions. The algorithm is based on the blow up method. It emphasizes the curves passing through the singular points and avoids the computation of the desingularized systems. Vector fields having a rational first integral are a particular case
Subject(s):	-Differential equations -planar analytic vector field -generalized rational first integral -blow up -Equacions diferencials ordinàries -Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
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Document type:	Article - Draft Report
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