Cantori for the stadium billiard.

Although almost all orbits in the stadium billiard are "chaotic," there are many regular orbits as well-the ordered periodic orbits and cantori. The symmetries of the stadium are exploited to find maximizing and saddle periodic orbits. Cantori are maximizing quasiperiodic orbits; they have caustics. Transport in the stadium should be impeded by cantori, just as in any twist map; this is particularly important for those orbits that are nearly glancing.