Bounded geodesics in moduli space

@inproceedings{Kleinbock2003BoundedGI,
  title={Bounded geodesics in moduli space},
  author={Dmitry Kleinbock and Barak Weiss},
  year={2003}
}
In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichm\"uller geodesic trajectories.The main tool is quantitative nondivergence of Teichm\"uller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons. 

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References

Publications referenced by this paper.
SHOWING 1-10 OF 16 REFERENCES

Logarithmic law for geodesics in moduli space

H. Masur
  • in: Mapping class groups and moduli spaces of Riemann surfaces, 229–245, Contemp. Math. 150, Amer. Math. Soc., Providence, RI
  • 1993
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Veech, Measures supported on the set of uniquely ergodic directions of an arbitrary holomorphic 1-form, Erg

W. A. Ve
  • Th. Dyn. Sys
  • 1999

Margulis, Flows on homogeneous spaces and Diophantine approximation on manifolds

G.A.D. Kleinbock
  • Ann. Math
  • 1998