STRUCTURAL STABILITY ON TWO-DIMENSIONAL MANIFOLDS

It is proved that the set S of all structurally stable vector fields is open and dense in B. B is the space of all vector fields or dynamical systems defined on a twodimensional compact differentiable manifold, M-squared. A vector field X is defined on M-squared is said to be structurally stable when a C(1)-small change in X does not change topologically the set of trajectories of X.