abstract:In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field, defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is a geometric manifestation of Hamilton's equations in classical mechanics.
In this paper, we considersome planar quintic HamiltonianvectorfieldwithZ3-equivariant property, getitsglobalphaseportraits, andclassify its parameterspace.