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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 1, Pages 186–216 (Mi izv2221)  

This article is cited in 63 scientific papers (total in 63 papers)

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.

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

Bibliographic databases:

UDC: 517.9
MSC: Primary 34C35; Secondary 52A10
Received: 07.02.1972

Citation: V. F. Lazutkin, “The existence of caustics for a billiard problem in a convex domain”, Izv. Akad. Nauk SSSR Ser. Mat., 37:1 (1973), 186–216; Math. USSR-Izv., 7:1 (1973), 185–214

Citation in format AMSBIB
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\by V.~F.~Lazutkin
\paper The existence of caustics for a~billiard problem in a~convex domain
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 1
\pages 186--216
\mathnet{http://mi.mathnet.ru/izv2221}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=328219}
\zmath{https://zbmath.org/?q=an:0256.52001}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 1
\pages 185--214
\crossref{https://doi.org/10.1070/IM1973v007n01ABEH001932}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
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