Year: 2019
Author: Huiyang Zhang, Aiyong Chen
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 2 : pp. 193–205
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.193
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 2 : pp. 193–205
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Hamiltonian systems nilpotent singular point global phase portraits Poincaré transformation.