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

Llibre, 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 -