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Local behavior of planar analytic vector fields via integrability |
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| Authors: | María Jesús Álvarez Antoni Ferragut |
| Affiliation: | 1. Departament de Matemàtiques i Informàtica, Universitat de les Illes Balears, Edifici Anselm Turmeda, Ctra. de Valldemossa, km 7.5, 07122 Palma, Illes Balears, Spain;2. Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Catalonia, Spain |
| 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. |
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