Psi-series of quadratic vector fields on the plane

Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability i...

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Detalles Bibliográficos
Autores: Delshams Valdés, Amadeu|||0000-0003-4134-8882, Mir, Arnau
Tipo de recurso: artículo
Fecha de publicación:1997
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:2117/875
Acceso en línea:https://hdl.handle.net/2117/875
Access Level:acceso abierto
Palabra clave:Differential equations
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34A General theory
Descripción
Sumario:Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic first integral is given.