Montserrat Corbera and Claudia Valls completely characterize the global phase portraits in the Poincaré disk for all planar Hamiltonian vector fields with linear plus cubic homogeneous terms having a nilpotent saddle at the origin.

 

 

Fig. 1. Global phase portraits of Hamiltonian planar polynomial vector fields with linear plus cubic homogeneous terms with a
nilpotent saddle at the origin. The separatrices are in bold.

https://doi.org/10.1016/j.nonrwa.2021.103451