Amadeu Delshams, Arnau Mir
Psi-Series of Quadratic Vector Fields on the Plane
(80K, LaTeX 2.09 and PicTeX)
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.