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The existence of caustics for a billiard problem in a convex domain

V. F. Lazutkin


Abstract: A system of caustics is found for a plane convex domain with a sufficiently smooth boundary; the caustics are close to the boundary and occupy a set of positive measure. A caustic is a convex smooth curve lying in the domain and possessing the property that a tangent to it becomes another tangent to the same curve after reflection from the boundary according to the law of geometrical optics.

UDC: 517.9

MSC: Primary 34C35; Secondary 52A10

Received: 07.02.1972

 English version: Mathematics of the USSR-Izvestiya, 1973, 7:1, 185–214

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