# Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.

Extracta Mathematicae (2006)

- Volume: 21, Issue: 2, page 167-190
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topLlibre, Jaume, and Pessoa, Claudio. "Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.." Extracta Mathematicae 21.2 (2006): 167-190. <http://eudml.org/doc/41857>.

@article{Llibre2006,

abstract = {Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.},

author = {Llibre, Jaume, Pessoa, Claudio},

journal = {Extracta Mathematicae},

keywords = {Sistemas dinámicos; Campos vectoriales; Quadratic homogeneous vector field; Invariant plane; limit cycle},

language = {eng},

number = {2},

pages = {167-190},

title = {Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.},

url = {http://eudml.org/doc/41857},

volume = {21},

year = {2006},

}

TY - JOUR

AU - Llibre, Jaume

AU - Pessoa, Claudio

TI - Homogeneous polynomial vector fields of degree 2 on the 2-dimensional sphere.

JO - Extracta Mathematicae

PY - 2006

VL - 21

IS - 2

SP - 167

EP - 190

AB - Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.

LA - eng

KW - Sistemas dinámicos; Campos vectoriales; Quadratic homogeneous vector field; Invariant plane; limit cycle

UR - http://eudml.org/doc/41857

ER -

## NotesEmbed ?

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