Rigid centres on the center manifold of tridimensional differential systems. Issue 4 (August 2022) - Mahdi, Adam; Pessoa, Claudio; Ribeiro, Jarne D.
Abstract : Motivated by the definition of rigid centres for planar differential systems, we introduce the study of rigid centres on the center manifolds of differential systems on $\mathbb {R}^{3}$ . On the plane, these centres have been extensively studied and several interesting results have been obtained. We present results that characterize the rigid systems on $\mathbb {R}^{3}$ and solve the centre-focus problem for several families of rigid systems.