



A chaotic orbit. The physical orbit of the billiard. 
The points in the phase space. 
An orbit on an invariant curve near the caustic. 
The points in the phase space is near the equator 




A whisper galery orbit. Existence is known by KAM theory. 
The orbit is near the boundary of the phase space 
A KAM curve around an elliptic periodic orbit. 
The orbit in the phase space lies on invariant curves 

Papers on families of billiards


