Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres - Buzzi, Claudio A. [UNESP]; Rodero, Ana Livia [UNESP]; Torregrosa, Joan (Springer Nature, 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.
Keywords: Center-focus problem; Integrability; Local cyclicity; Vector fields on invariant spheres