Polynomial Hamiltonian systems with a nilpotent critical point

Details Polynomial Hamiltonian systems with a nilpotent critical point Polynomial Hamiltonian systems with a nilpotent critical point

Aug 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010adspr..46..521h&link_type=abstract

Advances in Space Research, Volume 46, Issue 4, p. 521-525.

Physics

Space Physics

2

Scientific paper

The study of Hamiltonian systems is important for space physics and astrophysics. In this paper, we study local behavior of an isolated nilpotent critical point for polynomial Hamiltonian systems. We prove that there are exact three cases: a center, a cusp or a saddle. Then for quadratic and cubic Hamiltonian systems we obtain necessary and sufficient conditions for a nilpotent critical point to be a center, a cusp or a saddle. We also give phase portraits for these systems under some conditions of symmetry.

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