Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres
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The aim of this paper is the study of the center-focus and cyclicity problems inside the class X of 3-dimensional vector fields that admit a first integral that leaves invariant any sphere centered at the origin. We classify the centers of linear, quadratic homogeneous and a family of quadratic vector fields F⊂ X, restricted to one of these spheres. Moreover, we show the existence of at least 4 limit cycles in family F.
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Center-focus problem, Integrability, Local cyclicity, Vector fields on invariant spheres
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Inglês
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Journal of Nonlinear Science, v. 31, n. 6, 2021.
