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

Jaume Llibre, Claudio Pessoa (2006)

Extracta Mathematicae

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.

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