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On quadrilateral orbits in planar billiards

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  1. V. Ivrii, “The Second Term of the Spectral Asymptotics for a Laplace-Beltrami Operator on Manifolds with Boundary,” Func. Anal. Appl. 14, 98–106 (1980).

    Article  MathSciNet  Google Scholar 

  2. P. K. Rashevsky, Geometrical Theory of Partial Differential Equations (OGIZ Gostehizdat, Moscow, 1947).

    Google Scholar 

  3. M. R. Rychlik, “Periodic Points of the Billiard Ball Map in a Convex Domain,” J. Diff. Geom. 30, 191–205 (1989).

    MATH  MathSciNet  Google Scholar 

  4. Ya. B. Vorobets, “On the Measure of the Set of Periodic Points of a Billiard,” Math. Notes 55, 455–460 (1994) [Mat. Zamet. 55, 25–35 (1994)].

    Article  MathSciNet  Google Scholar 

  5. H. Weyl, Gesammelte Abhandlungen (Springer-Verlag, Berlin, 1968).

    MATH  Google Scholar 

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Published in Russian in Doklady Akademii Nauk, 2011, Vol. 438, No. 5, pp. 590–592.

The article was translated by the authors.

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Glutsyuk, A.A., Kudryashov, Y.G. On quadrilateral orbits in planar billiards. Dokl. Math. 83, 371–373 (2011).

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  • Periodic Orbit
  • Analytic Continuation
  • Smooth Boundary
  • Periodic Point
  • Measure Zero