Geodesic
The existence of caustics for a~billiard problem in a~convex domain
Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 185-214

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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. 
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     author = {V. F. Lazutkin},
     title = {The existence of caustics for a~billiard problem in a~convex domain},
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V. F. Lazutkin. The existence of caustics for a~billiard problem in a~convex domain. Izvestiya. Mathematics , Tome 7 (1973) no. 1, pp. 185-214. http://geodesic.mathdoc.fr/item/IM2_1973_7_1_a8/