Billiards on rational-angled triangles

Commentarii Mathematici Helvetici

Volumn 75, Issue 1, 2000, Pages 65-108

  Kenyon, Richard ^a,b   Smillie, John ^c  

^a UNIVERSITÉ DE LYON   (France)

^b UNIVERSITÉ PARIS SUD   (France)

^c Department of Molecular Biology and Genetics   (United States)

Author keywords

Polygonal billiards; Veech examples

Indexed keywords

EID: 0007404656     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000140050113     Document Type: Article

References (34)

1. A. D. Alexandrov, V. N. Berestovski and I. G. Nikolaev, Russian Math. Surveys 41 (3) (1986), 1-54.
2. V. I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, 1978.
3. ecycle, Université de Reims, 1981.
4. B. Bowditch, Singular Euclidean structures on surfaces J. London Math Soc. 44 (1991), 553-565.
5. M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, in preparation.
6. K. Brown, Cohomology of Groups, Springer-Verlag 1982.
7. M. V. Berry and P. J. Richens, Pseudointegrable systems in classical and quantum mechanics, Physica D 2(3) (1981), 495-512.
8. C. J. Earle, F. P. Gardiner, Teichmuller disks and Veech's ℱ-structures. Extremal Riemann surfaces 165-189 Contemp. Math., 201 AMS Providence, RI, 1997.
9. A. Fathi, Some compact invariant sets for hyperbolic linear automorphisms of tori, Erg. Th. & Dyn. Sys. 8 (1988), 191-204.
10. L. Ford, Automorphic Functions, Chelsea Publishing Company, New York 1929 (reprinted 1972).
11. J. Franks and E. Rykken, Pseudo-Anosov homeomorphisms with quadratic expansion, (to appear Proc. of the A.M.S.).
12. D. Fried, Growth rate of surface homeomorphisms and flow equivalence. Erg. Th. & Dyn. Syst. 5(4) (1985), 539-563.
13. E. Gutkin, Billiards in almost integrable polyhedral surfaces. Erg. Th. & Dyn. Syst. 4 (1984), 569-584.
14. E. Gutkin and C. Judge, The geometry and arithmetic of translation surfaces with applications to polygonal billiards, Math. Res. Lett. 3 (1996), 391-403.
15. E. Gutkin and C. Judge, Affine mappings of translation surfaces: geometry and arithmetic, preprint (1997).
16. R. Kenyon, Tilings and discrete Dirichlet problems. Isr. J. Math 105 (1998), 61-84.
17. R. Kirby, Problems in low dimensional manifold theory, in Proceed, of Symp. in Pure Math. 32 (1978), 273-312.
18. G. Levitt, Propriètés homologiques des feuilletages des surfaces, C.R. Acad. Sci Paris Sér. I Math. 293 (1981), 597-600.
19. H. Masur, J. Smillie. Hausdorff dimension of sets of nonergodic measured foliations Annals of Math. 134 (1991), 455-543.
20. C. H. Sah, Hilbert's third problem: scissors congruence. Research Notes in Mathematics, 33. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. vi+188 pp.
21. C. H. Sah, Scissors congruence of the interval, preprint.
22. S. Schwartzman, Asymptotic cycles. Ann. of Math. 66(2) (1957), 270-284.
23. S. Tabachnikoff, Billiards. Panoramas et Synthèses 1 Soc. Math. France (1995).
24. W.P. Thurston, Shapes of polyhedra, preprint.
25. M. Troyanov, Les surfaces euclidiennes à singulariéts coniques. (French) [Euclidean surfaces with conical singularities] Enseign. Math. 32(2) (1986), no. 1-2, 79-94.
26. W. A. Veech, Teichmuller curves in modular space, Eisenstein series, and an application to triangular billiards, Inventiones Math. 97 (1989), 553-583.
27. W. A. Veech, The billiard in a regular polygon, Geom. Func. Anal. 2 (1992), 341-379.
28. Ya. B. Vorobets, Plane structures and billiards in rational polyhedra. (Russian) Uspekhi Mat. Nauk 51(1) (1996), 145-146; translation in Russian Math. Surveys 51(1) (1996), 177-178.
29. Ya. B. Vorobets, Plane structures and billiards in rational polyhedra. (Russian) Uspekhi Mat. Nauk 51(1) (1996), 145-146; translation in Russian Math. Surveys 51(1) (1996), 177-178.
30. Ya. B. Vorobets, Plane structures and billiards in rational polygons: the Veech alternative. (Russian) Uspekhi Mat. Nauk 51(5) (1996), 3-42. translation in Russian Math. Surveys 51(5) (1996), 779-817.
31. Ya. B. Vorobets, Plane structures and billiards in rational polygons: the Veech alternative. (Russian) Uspekhi Mat. Nauk 51(5) (1996), 3-42. translation in Russian Math. Surveys 51(5) (1996), 779-817.
32. C. Ward, Fuchsian groups and polygonal billiards, Thesis, Rice University 1996.
33. A. Zemlyakov, A. Katok. Topological transitivity of billiards in polygons, Math. Notes of the USSR Acad. Sci. 18(2) (1975), 291-300. (English translation in Math. Notes 18(2) (1976), 760-764.)
34. A. Zemlyakov, A. Katok. Topological transitivity of billiards in polygons, Math. Notes of the USSR Acad. Sci. 18(2) (1975), 291-300. (English translation in Math. Notes 18(2) (1976), 760-764.)