Rigid centres on the center manifold of tridimensional differential systems

Mahdi, AdamPessoa, Claudio [UNESP]Ribeiro, Jarne D.2022-04-292022-04-292021-01-01Proceedings of the Royal Society of Edinburgh Section A: Mathematics.1473-71240308-2105http://hdl.handle.net/11449/229528Motivated 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 ℝ3. 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 ℝ3 and solve the centre-focus problem for several families of rigid systems.engcenter manifoldCentre-focus problemfirst integralrigid centreRigid centres on the center manifold of tridimensional differential systemsArtigo10.1017/prm.2021.462-s2.0-85115025843