0 used in or relating to billiards (= a game played by two people on a table covered in green cloth, in which a long stick is used to hit balls into pockets around the table): --
An example of this situation is given by the usual billiard in an ellipse; the billiard transformation has an invariant area form.
The billiard transformation is defined in metric terms (equal angles), and, in particular, it is not equivariant under projective transformations of the plane.
The transformation in question is a projective billiard transformation, the transversals being the normals to in the metric under consideration.
The connected configuration space of a so-called cylindric billiard system is a flat torus minus finitely many spherical cylinders.
Thus, we obtained that any cylindric billiard with one-dimensional generators is necessarily tight, unless all generators are parallel.
That theory is already applicable for billiard systems, too.
In this paper we show that the topological entropy of a compact non-degenerate semidispersing billiard on any manifold of non-positive sectional curvature is finite.
In [6], it is shown that the topological entropy of a compact non-degenerate semi-dispersing billiard on any manifold of non-positive sectional curvature is finite.
