Center problem for generic degenerate vector fields. (January 2022)

• Record Type: Journal Article
• Authors: Algaba, Antonio; Díaz, María; García, Cristóbal; Giné, Jaume
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: Center problem -- Degenerate vectors -- Monodromy -- Characteristic directions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112597
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We generalize the method of construction of an integrating factor for Abel differential equations, developed in Briskin et al. (1998), for any generic monodromic singularity. Here generic means that the vector field has not characteristic directions in the quasi-homogeneous leading term in certain coordinates. We apply this method to some degenerate differential systems.