© 2017 International Association for Mathematics and Computers in Simulation (IMACS) We provide normal forms and the global phase portraits in the Poincaré disk for all Hamiltonian planar polynomial vector fields of degree 3 symmetric with respect to the x-axis having a nilpotent center at the origin.
- Nilpotent center
- Phase portrait
- Poincaré compactification
- Polynomial Hamiltonian systems