Local behavior of planar analytic vector fields via integrability

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 computa...

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Detalles Bibliográficos
Autores: Ferragut Amengual, Antoni Manel, Álvarez, María Jesús
Tipo de recurso: informe técnico
Fecha de publicación:2009
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/6506
Acceso en línea:https://hdl.handle.net/2117/6506
Access Level:acceso abierto
Palabra clave:Differential equations
planar analytic vector field
generalized rational first integral
blow up
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Descripción
Sumario: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