Theorem 1.1 (Jordan Curve Theorem):

A simple closed curve separates the plane into two disjoint open connected sets precisely one of which is bounded.

The theorem was used by Jordan in his formulation of Cauchy's theorem. Though the Jordan curve theorem no longer plays a central rôle in complex function theory it is nevertheless

Figure: Simple closed curve

[width=.4]GKSBook/fig1/fig1.eps

indispensable in many other branches such as ordinary differential equations. Let us consider the (non-trivial) problem of locating periodic solutions of systems of differential equations. In planar domains, a useful criterion is given by the following