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Moscow Mathematical Journal, 2006, Volume 6, Number 4, Pages 673–701
DOI: https://doi.org/10.17323/1609-4514-2006-6-4-673-701 (Mi mmj265) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature

E. A. Gutkinab, S. L. Tabachnikovc

a Instituto Nacional de Matemática Pura e Aplicada
b University of California, Los Angeles
c Department of Mathematics, Pennsylvania State University
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DOI: https://doi.org/10.17323/1609-4514-2006-6-4-673-701
Abstract: We introduce piecewise convex transformations, and develop geometric tools to study their complexity. We apply the results to the complexity of polygonal inner and outer billiards on surfaces of constant curvature.
Key words and phrases: Geodesic polygon, constant curvature, complexity, inner billiard, outer billiard.
Received: April 29, 2006; in revised form October 16, 2006
Bibliographic databases:
MSC: 53D25, 37E99, 37B10
Language: English
Citation: E. A. Gutkin, S. L. Tabachnikov, “Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature”, Mosc. Math. J., 6:4 (2006), 673–701
Citation in format AMSBIB
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\by E.~A.~Gutkin, S.~L.~Tabachnikov
\paper Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards on surfaces of constant curvature
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 4
\pages 673--701
\mathnet{http://mi.mathnet.ru/mmj265}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-4-673-701}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2291158}
\zmath{https://zbmath.org/?q=an:1123.53043}
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    • This publication is cited in the following 11 articles:
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