Asymptotic formulas on flat surfaces

Ergodic Theory and Dynamical Systems

Volumn 21, Issue 2, 2001, Pages 443-478

  Eskin, Alex ^a   Masur, Howard ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035635339     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385701001225     Document Type: Article

References (24)

1. C. Earle and F. Gardiner. Teichmuller disks and Veech's ℱ-structures. Extremal Riemann surfaces (San Francisco, CA, 1995) (Contemp. Math., 201). American Mathematical Society, Providence, RI, 1997, pp. 165-189.
2. A. Eskin, H. Masur and M. Schmoll. In preparation.
3. A. Eskin, G. Margulis and S. Mozes. Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture. Ann. Math. 147(1) (1998), 93-141.
4. A. Eskin, H. Masur and A. Zorich. The Siegel-Veech constants. In preparation.
5. A. Eskin and A. Okounkov. Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials. Preprint.
6. A. Eskin and A. Zorich. Billiards in right-angled polygons. In preparation.
7. E. Gutkin. Billiards on almost integrable polyhedral surfaces. Ergod. Th. & Dynam. Sys. 4 (1984), 569-584.
8. E. Gutkin and C. Judge. Affine mappings of translation surfaces: geometry and arithmetic. Preprint.
9. S. Kerckhoff, H. Masur and J. Smillie. Ergodicity of billiard flows and quadratic differentials. Ann. Math. 124 (1986), 293-311.
10. M. Kontsevich and A. Zorich. Connected components of the space of holomorphic differentials with prescribed singularities. Preprint.
11. I. Kra. On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces. Acta Math. 146(3-4) (1981), 231-270.
12. H. Masur. Interval exchange transformations and measured foliations. Ann. Math. 115 (1982), 169-200.
13. H. Masur. The growth rate of trajectories of a quadratic differential. Ergod. Th. & Dynam. Sys. 10 (1990), 151-176.
14. H. Masur. Lower bounds for the number of saddle connections and closed trajectories of a quadratic quadratic differential. Holomorphic Functions and Moduli, Vol. 2. Springer, Berlin, 1988.
15. H. Masur and J. Smillie. Hausdorff dimension of sets of foliations. Ann. Math. 134 (1991), 455-543.
16. A. Nevo and E. Stein. Pointwise ergodic theorems for radial averages on simple Lie groups II. Duke Math. J. 86 (1997), 239-259.
17. A. Nevo. Equidistribution in measure preserving actions of semisimple groups. Preprint.
18. M. Ratner. On Raghunathan's measure conjecture. Ann. Math. 134 (1991), 545-607.
19. W. Veech. Gauss measures for transformations on the space of interval exchange maps. Ann. Math. 115(1) (1982), 201-242.
20. W. Veech. The Teichmuller geodesic flow. Ann. Math. 124(3) (1986), 441-530.
21. W. Veech. Teichmuller curves in moduli space, Eisenstein series and an application to triangular billiards. Invent. Math. 97(3) (1989), 553-583.
22. W. Veech. Moduli spaces of quadratic differentials. J. Analyse. Math. 55 (1990), 117-171.
23. W. Veech. Siegel measures. Ann. Math. 148 (1998), 895-944.
24. A. N. Zemlyakov and A. B. Katok. Topological transitivity of billiards in polygons. Matem. Zametki 18(2) (1975), 291-300. (Eng. Transl. Math. Notes 18(2) (1976), 760-764).