Global Phase Portraits of Symmetrical Cubic Hamiltonian Systems with a Nilpotent Singular Point (Journal of Nonlinear Modeling and Analysis, 2024)
Han et al. [Han et al., Polynomial Hamiltonian systems with anilpotent critical point, J. Adv. Space Res. 2010, 46, 521–525] successfullystudied local behavior of an isolated nilpotent critical point for polynomialHamiltonian systems. In this paper, we extend the previous result by analyzingthe global phase portraits of polynomial Hamiltonian systems. We provide 12non-topological equivalent classes of global phase portraits in the Poincaré diskof cubic polynomial Hamiltonian systems with a nilpotent center or saddle atorigin under some conditions of symmetry.
Keywords: Hamiltonian systems; nilpotent singular point; global phase portraits; Poincaré transformation.