Skip to main content

On quadrilateral orbits in planar billiards

Doklady Mathematics volume 83, pages 371–373 (2011)Cite this article

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  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 

Download references

Author information

Authors and Affiliations

  1. IUM, Poncelet Laboratory, Independent Moscow University, Moscow, Russia

    A. A. Glutsyuk & Yu. G. Kudryashov

  2. CNRS, Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, Lyon, France

    A. A. Glutsyuk & Yu. G. Kudryashov

Authors
  1. A. A. Glutsyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. G. Kudryashov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

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

The article was translated by the authors.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Glutsyuk, A.A., Kudryashov, Y.G. On quadrilateral orbits in planar billiards. Dokl. Math. 83, 371–373 (2011). https://doi.org/10.1134/S1064562411030343

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562411030343

Keywords

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