0 a game played by two people on a table covered in green cloth, in which a cue (= a long stick) is used to hit balls against each other and into pockets around the table -- 撞球運動
Next we turn our attention to projective billiards in a circle.
These curves form a large family of focusing curves that can be used to construct hyperbolic billiards.
Note that for cylindrical semi-focusing billiards, the same happens for consecutive collisions with the flat boundary components.
To obtain our results, we will re-prove in a more general setting many technical results established earlier for semi-dispersing hyperbolic billiards.
All three papers address various problems in the theory of semi-dispersing billiards using the geometric approach outlined above.
Our proof can be readily extended to a broader class of cylindrical billiards, and very likely to other highdimensional billiards (see 5).
The motivation for these definitions, in the realm of billiards, is the following.
Estimates like that play an important role in various questions about billiards.
