Psi-series of quadratic vector fields on the plane.

Delshams, Amadeu, and Mir, Arnau. "Psi-series of quadratic vector fields on the plane.." Publicacions Matemàtiques 41.1 (1997): 101-125. <http://eudml.org/doc/41287>.

@article{Delshams1997,
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.},
author = {Delshams, Amadeu, Mir, Arnau},
journal = {Publicacions Matemàtiques},
keywords = {Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Series sumables; Función logarítmica; logarithm singularities; quadratic systems; psi-series; Painlevé principle},
language = {eng},
number = {1},
pages = {101-125},
title = {Psi-series of quadratic vector fields on the plane.},
url = {http://eudml.org/doc/41287},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Delshams, Amadeu
AU - Mir, Arnau
TI - Psi-series of quadratic vector fields on the plane.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 1
SP - 101
EP - 125
AB - 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.
LA - eng
KW - Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Series sumables; Función logarítmica; logarithm singularities; quadratic systems; psi-series; Painlevé principle
UR - http://eudml.org/doc/41287
ER -