Bifurcation diagrams for Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields
In [Adv. Math. 259, 655--687 (2014; Zbl 1303.34027)], the authors provided the normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian nilpotent centers of linear plus cubic homogeneous planar polynomial vector fields. In [J. Math. Anal. Appl. 433, No. 1, 305--319 (2016; Zbl 1336.34047)], \textit{M. Dukarić} et al. provided the global phase portraits in the Poincaré disk for all reversible nilpotent centers with cubic homogeneous nonlinearities planar polynomial vector fields. These two works complete the classification of the phase portraits of the nilpotent centers with cubic homogeneous nonlinearities. In the present work, the authors give the bifurcation diagrams for the global phase portraits in the Poincaré disk of the first planar polynomial vector fields.
scientific article; zbMATH DE number 6695505
scientific article