Each resonance consists of a chain of n islands and each island
has a structure similar to the pendulum.
Perturbation theory implies that the width of the m/n resonance
grows as K n/2 for K small. At the center of the
island, and at the cusp of the separatrix, are periodic orbits with
frequency m/n . Typically there appear to be only two such periodic
Orbits trapped in an island move successively from one island to another,
following the periodic orbit (they skip m-1 islands each step). Thus
there is an entire region of phase space that has frequency m/n .