Local behavior of planar analytic vector fields via integrability
Álvarez Torres, María Jesús (Universitat de les Illes Balears. Departament de Ciències Matemàtiques i Informàtica)
Ferragut Amengual, Antoni Manel (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)

Date:	2012
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.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: AF is additionally partially supported by grants Juan de la Cierva MTM2009-14163-C02-02.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Planar analytic vector field ; Generalized rational first integral ; Blow up
Published in:	Journal of mathematical analysis and applications, Vol. 385 (2012) , p. 264-277, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2011.06.062

Postprint 18 p, 424.3 KB

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