AFFINE MAPPINGS OF TRANSLATION SURFACES : GEOMETRY AND ARITHMETIC

@inproceedings{Gutkin2000AFFINEMO,
  title={AFFINE MAPPINGS OF TRANSLATION SURFACES : GEOMETRY AND ARITHMETIC},
  author={Eugene Gutkin and Chris Hope Judge},
  year={2000}
}
1. Introduction. Translation surfaces naturally arise in the study of billiards in rational polygons (see [ZKa]). To any such polygon P , there corresponds a unique translation surface, S = S(P), such that the billiard flow in P is equivalent to the geodesic flow on S (see, e.g., [Gu2], [Gu3]). There is also a classical relation between translation surfaces and quadratic differentials on a Riemann surface S. Namely, each quadratic differential induces a translation structure on a finite… CONTINUE READING
Highly Cited
This paper has 383 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 13 references

Billiards in polygons : Survey of recent results

  • GuJ E. Gutkin, C. Judge
  • J . Statist . Phys .
  • 1996

Lower bounds for the number of saddle connections and closed trajectories of a quadratic differential

  • H. Masur
  • inHolomorphic Functions and Moduli I (Berkeley…
  • 1996

Zemlyakov and A . Katok , Topological transitivity of billiards in polygons

  • A. ZKa
  • Math . Notes
  • 1996

Geometry

  • M. Berger
  • Universitext, Springer, Berlin
  • 1994

Plane structures and billiards in rational polyhedra , Russ

  • Ya. Vorobets
  • Math . Surv .
  • 1992

Hausdorff dimension of sets of nonergodic measured foliations

  • H. Masur, J. Smillie
  • Ann. of Math
  • 1991

Singular euclidean structures on surfaces

  • Bo B. Bowditch
  • J . LondonMath . Soc .
  • 1991

Teichmüller curves in moduli space, Eisenstein series, and an application to triangular billiards, Invent

  • W. Veech
  • 1989

Discrete groups with dense orbits [ Appendix ]

  • L. Auslander, L. Green, F. Hahn
  • 1963