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