# Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 335-356
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topChavarriga, Javier, and Giné, Jaume. "Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.." Publicacions Matemàtiques 41.2 (1997): 335-356. <http://eudml.org/doc/41322>.

@article{Chavarriga1997,

abstract = {In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.},

author = {Chavarriga, Javier, Giné, Jaume},

journal = {Publicacions Matemàtiques},

keywords = {Sistemas diferenciales; Polinomios; Sistemas bidimensionales; Invariantes; center; integrability; planar polynomial differential systems; Lyapunov constants},

language = {eng},

number = {2},

pages = {335-356},

title = {Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.},

url = {http://eudml.org/doc/41322},

volume = {41},

year = {1997},

}

TY - JOUR

AU - Chavarriga, Javier

AU - Giné, Jaume

TI - Integrability of a linear center perturbed by a fifth degree homogeneous polynomial.

JO - Publicacions Matemàtiques

PY - 1997

VL - 41

IS - 2

SP - 335

EP - 356

AB - In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

LA - eng

KW - Sistemas diferenciales; Polinomios; Sistemas bidimensionales; Invariantes; center; integrability; planar polynomial differential systems; Lyapunov constants

UR - http://eudml.org/doc/41322

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.