Analytic integrability inside a family of degenerate centers. (October 2016)

• Record Type: Journal Article
• Authors: Algaba, Antonio; Checa, Isabel; García, Cristóbal; Giné, Jaume
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 288
• Page End: 307
• Publication Date: 2016-10
• Subjects: Nonlinear differential systems -- Integrability problem -- Degenerate center problem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.02.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we study the analytic integrability around the origin inside a family of degenerate centers or perturbations of them. For this family analytic integrability does not imply formal orbital equivalence to a Hamiltonian system. It is shown how difficult is the integrability problem even inside this simple family of degenerate centers or perturbations of them.