Algebraic integrability of nilpotent planar vector fields. (April 2021)

• Record Type: Journal Article
• Authors: Algaba, A.; García, C.; Reyes, M.
• Is Part Of: Chaos, solitons and fractals. Volume 145(2021)
• Publication Date: 2021-04
• Subjects: Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110765
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: We characterize, using normal forms of quasi-homogeneous expansions, the analytic vector fields at nilpotent singular point having an algebraic first integral over the ring C [ [ x, y ] ] . As a consequence, we provide a link between the algebraic integrability problem and the existence of a formal inverse integrating factor which is null at the singular point.