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

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

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.

Author Details

Huiyang Zhang

Aiyong Chen