Ergodicity of billiard flows and quadratic differentials. (English) Zbl 0637.58010

Kerckhoff, Steven; Masur, Howard; Smillie, John

Ann. Math. (2) 124, 293-311 (1986).

The paper is concerned with polygonal billiards in the plane. Its main result is that the set of polygons with an ergodic billiard flow contains a dense \(G_{\delta}\). It is obtained as a corollary of a result the authors prove about Riemannian surfaces and quadratic differentials.

Reviewer: H.Crauel

MSC:

37A99	Ergodic theory
30F99	Riemann surfaces

Keywords:

polygonal billiards; ergodic billiard flow