Global Phase Portraits of Symmetrical Cubic Hamiltonian Systems with a Nilpotent Singular Point

Abstract

Han et al. [Han et al., Polynomial Hamiltonian systems with a nilpotent critical point, J. Adv. Space Res. 2010, 46, 521–525] successfully studied local behavior of an isolated nilpotent critical point for polynomial Hamiltonian systems. In this paper, we extend the previous result by analyzing the global phase portraits of polynomial Hamiltonian systems. We provide 12 non-topological equivalent classes of global phase portraits in the Poincaré disk of cubic polynomial Hamiltonian systems with a nilpotent center or saddle at origin under some conditions of symmetry.