TY - JOUR
T1 - Global Phase Portraits of Symmetrical Cubic Hamiltonian Systems with a Nilpotent Singular Point
AU - Zhang , Huiyang
AU - Chen , Aiyong
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 193
EP - 205
PY - 2021
DA - 2021/04
SN - 1
DO - http://doi.org/10.12150/jnma.2019.193
UR - https://global-sci.org/intro/article_detail/jnma/18857.html
KW - Hamiltonian systems, nilpotent singular point, global phase portraits, Poincaré transformation.
AB - <p style="text-align: justify;">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.</p>