dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author
Delshams Valdés, Amadeu
dc.contributor.author
Mir, Arnau
dc.identifier
https://hdl.handle.net/2117/875
dc.description.abstract
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.
dc.format
application/pdf
dc.rights
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
dc.rights
Attribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject
Differential equations
dc.subject
Equacions diferencials ordinàries
dc.subject
Equacions diferencials ordinàries
dc.subject
Classificació AMS::34 Ordinary differential equations::34A General theory
dc.title
Psi-series of quadratic vector fields on the plane
