Skip to main content
SpringerLink
Log in

Deloné property of the holonomy vectors of translation surfaces

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We answer a question posed by Barak Weiss on the uniform discreteness of the set of the holonomy vectors of translation surfaces.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. S. Athreya and J. Chaika, The distribution of gaps for saddle connection directions, Geometric and Functional Analysis 22 (2012), 1491–1516.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. S. Athreya, J. Chaika and S. Lelievre, The gap distribution of slopes on the golden L, Contemporary Mathematics 631 (2015), 47–62.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. S. Dani, Density properties of orbits under discrete groups, Journal of the Indian Mathematical Society 39 (1975), 189–218.

    MathSciNet  MATH  Google Scholar 

  4. A. Eskin and H. Masur, Asymptotic formulas on flat surfaces, Ergodic Theory and Dynamical Systems 21 (2001), 443–478.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Herzog and B. M. Stewart, Patterns of visible and nonvisible lattice points, American Mathematical Monthly 78 (1971), 487–496.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Kenyon and J. Smillie, Billiards on rational-angled triangles, Commentarii Mathematici Helvetici 75 (2000), 65–108.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Masur, Lower bounds for the number of saddle connections and closed trajectories of a quadratic differential, in Holomorphic Functions and Moduli. I (Berkeley, CA, 1986), Mathematical Sciences Research Institute Publications, Vol. 10, Springer, New York, 1988, pp. 215–228.

    Google Scholar 

  8. H. Masur, The growth rate of trajectories of a quadratic differential, Ergodic Theory and Dynamical Systems 10 (1990), 151–176.

    Article  MathSciNet  MATH  Google Scholar 

  9. C. T. McMullen, Dynamics of SL2 (R) over moduli space in genus two, Annals of mathematics 165 (2007), 397–456.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Senechal, What is... a quasicrystal, Notices of the American Mathematical Society 53 (2006), 886–887.

    MathSciNet  MATH  Google Scholar 

  11. J. Smillie and B. Weiss, Characterizations of lattice surfaces, Inventiones mathematicae 180 (2010), 535–557.

    Article  MathSciNet  MATH  Google Scholar 

  12. W. A. Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Inventiones mathematicae 97 (1989), 553–583.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Chenxi Wu

Authors
  1. Chenxi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chenxi Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, C. Deloné property of the holonomy vectors of translation surfaces. Isr. J. Math. 214, 733–740 (2016). https://doi.org/10.1007/s11856-016-1357-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-016-1357-y

Search

Navigation