Structural Stability of Planar Hamiltonian Polynomial Vector Fields

We characterize the set of all structurally stable planar Hamiltonian polynomial vector fields with respect to perturbations, first in the set of all Cr planar vector fields, second in the set of all planar polynomial vector fields, and third in the set of all planar Hamiltonian polynomial vector fields. We also classify the canonical regions of the structurally stable planar Hamiltonian polynomial vector fields, and study its genericity. © 1994 The London Mathematical Society.