Centers and limit cycles of vector fields defined on invariant spheres - Buzzi, Claudio A; Rodero, Ana Livia; Torregrosa, Joan (Springer, 2021)
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.
This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00332-021-09751-z.
Keywords: Vector fields on invariant spheres; Integrability; Center-focus problem; Local cyclicity