Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.

Giacomini, Hector, and Ndiaye, Malick. "Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.." Publicacions Matemàtiques 40.1 (1996): 205-214. <http://eudml.org/doc/41244>.

@article{Giacomini1996,
abstract = {In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part.For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type.By induction, we have been able to generalize these results for polynomial systems of arbitrary degree.},
author = {Giacomini, Hector, Ndiaye, Malick},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones diferenciales; Curvas algebraicas planas; Ecuaciones polinómicas; Puntos críticos; centers; autonomous polynomial system; Mathematica; symbolic computation},
language = {eng},
number = {1},
pages = {205-214},
title = {Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.},
url = {http://eudml.org/doc/41244},
volume = {40},
year = {1996},
}

TY - JOUR
AU - Giacomini, Hector
AU - Ndiaye, Malick
TI - Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.
JO - Publicacions Matemàtiques
PY - 1996
VL - 40
IS - 1
SP - 205
EP - 214
AB - In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part.For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type.By induction, we have been able to generalize these results for polynomial systems of arbitrary degree.
LA - eng
KW - Ecuaciones diferenciales; Curvas algebraicas planas; Ecuaciones polinómicas; Puntos críticos; centers; autonomous polynomial system; Mathematica; symbolic computation
UR - http://eudml.org/doc/41244
ER -