On topological entropy of billiard tables with small inner scatterers (Q968811)

The author studies the topological entropy of a class of billiard systems, which consists of strictly convex domain in the plane and strictly convex inner scatters. The author proves that the topological entropy of the first return map to the scatters can be made arbitrarily large provided the inner scatters are sufficiently small. The author uses the concept of anti-integrable limits with the theory of Lyusternik-Shnirel'man. These results generalize C. Foltin's result which states that ``there is an open and dense subset of the billiard space with \(K\geq 1\) (the number of convex scatters) in which every billiard flow has positive topological entropy provided the inner scatters are small enough''.