Rigid centres on the center manifold of tridimensional differential systems. Issue 4 (August 2022)

• Record Type: Journal Article
• Authors: Mahdi, Adam; Pessoa, Claudio; Ribeiro, Jarne D.
• Is Part Of: Proceedings. Volume 152:Issue 4(2022)
• Page Start: 1058
• Page End: 1080
• Publication Date: 2022-08
• Subjects: Centre-focus problem -- center manifold -- first integral -- rigid centre; 34C05 -- 34A34; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2021.46
• Languages: English
• ISSNs: 0308-2105

Abstract

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.