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Sbornik: Mathematics, 1997, Volume 188, Issue 3, Pages 389–434
DOI: https://doi.org/10.1070/sm1997v188n03ABEH000211 (Mi sm211) 		 
This article is cited in 24 scientific papers (total in 24 papers)

Ergodicity of billiards in polygons

Ya. B. Vorobets

M. V. Lomonosov Moscow State University
English version PDF (443 kB) Citations (24)
References:
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DOI: https://doi.org/10.1070/sm1997v188n03ABEH000211
Abstract: In the space of all polygons, a topologically massive subset consisting of polygons with ergodic billiard flows is explicitly described. The elements of this set have a specified order of approximation by rational polygons. As intermediate results, constructive versions of the ergodic theorem for the billiard in a rational polygon and for the geodesic flow on a surface with flat structure, and also a constructive quadratic estimate for the growth of the number of saddle connections (singular trajectories) in a flat structure, are proved.
Received: 20.06.1996
Russian version:
Matematicheskii Sbornik, 1997, Volume 188, Number 3, Pages 65–112
DOI: https://doi.org/10.4213/sm211
Bibliographic databases:
UDC: 517.987.5
MSC: 58F11, 58F17
Language: English
Original paper language: Russian
Citation: Ya. B. Vorobets, “Ergodicity of billiards in polygons”, Mat. Sb., 188:3 (1997), 65–112; Sb. Math., 188:3 (1997), 389–434
Citation in format AMSBIB
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:13
    References:71
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