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

Hector Giacomini; Malick Ndiaye

Publicacions Matemàtiques (1996)

- Volume: 40, Issue: 1, page 205-214
- ISSN: 0214-1493

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topGiacomini, 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 -

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