The center and cyclicity problems for quartic linear-like reversible systems. (January 2020)

• Record Type: Journal Article
• Authors: da Cruz, Leonardo P.C.; Romanovski, Valery G.; Torregrosa, J.
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: primary 34C07 34C23 37C27; Center-focus problem -- Linear-like reversible centers -- Quartic centers -- Center cyclicity; 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.2019.111593
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study a family of quartic linear-like reversible polynomial systems having a nondegenerate center at the origin. This family has degree one with respect to one of the variables. We are interested in systems in this class having two extra nondegenerate centers outside the straight line of symmetry. The geometrical configuration of these centers is aligned or triangular. We solve the center problem in both situations and, in the second case, we study the limit cycles obtained from a simultaneous degenerate Hopf bifurcation in the quartic polynomials class.