Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1765346 | Advances in Space Research | 2010 | 5 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Earth and Planetary Sciences
Space and Planetary Science
Authors
Maoan Han, Chenggang Shu, Junmin Yang, Abraham C.-L. Chian,