Nilpotent Centers of a Cubic System Reducible to a Nonlinear Vibration System

Algebraic integrability of nilpotent planar vector fields

“…For example, Sadovskii [31] , Berthier and Moussu [11] , Andreev et al [10] , Giacomini et al [21] , García et al [20] , Algaba et al [4] have characterized the nilpotent centers. The center problem has been solved for some families, see [9,16,24] . Particularly, Chavarriga et al [13] and García and Giné [19] study the analytically integrable nilpotent centers.…”