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

Billiards on rational-angled triangles

Author keywords

Polygonal billiards; Veech examples

Indexed keywords


EID: 0007404656     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000140050113     Document Type: Article
Times cited : (104)

References (34)
  • 3
    • 0040017312 scopus 로고
    • ecycle, Université de Reims
    • ecycle, Université de Reims, 1981.
    • (1981)
    • Arnoux, P.1
  • 4
    • 0005337752 scopus 로고
    • Singular Euclidean structures on surfaces
    • B. Bowditch, Singular Euclidean structures on surfaces J. London Math Soc. 44 (1991), 553-565.
    • (1991) J. London Math Soc. , vol.44 , pp. 553-565
    • Bowditch, B.1
  • 7
    • 49049152047 scopus 로고
    • Pseudointegrable systems in classical and quantum mechanics
    • M. V. Berry and P. J. Richens, Pseudointegrable systems in classical and quantum mechanics, Physica D 2(3) (1981), 495-512.
    • (1981) Physica D , vol.2 , Issue.3 , pp. 495-512
    • Berry, M.V.1    Richens, P.J.2
  • 8
    • 0039468246 scopus 로고    scopus 로고
    • Teichmuller disks and Veech's ℱ-structures
    • Extremal Riemann surfaces, AMS Providence, RI
    • 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.
    • (1997) Contemp. Math. , vol.201 , pp. 165-189
    • Earle, C.J.1    Gardiner, F.P.2
  • 9
    • 84974264683 scopus 로고
    • Some compact invariant sets for hyperbolic linear automorphisms of tori
    • A. Fathi, Some compact invariant sets for hyperbolic linear automorphisms of tori, Erg. Th. & Dyn. Sys. 8 (1988), 191-204.
    • (1988) Erg. Th. & Dyn. Sys. , vol.8 , pp. 191-204
    • Fathi, A.1
  • 10
    • 0003610679 scopus 로고
    • Chelsea Publishing Company, New York reprinted
    • L. Ford, Automorphic Functions, Chelsea Publishing Company, New York 1929 (reprinted 1972).
    • (1929) Automorphic Functions
    • Ford, L.1
  • 11
    • 0039424937 scopus 로고    scopus 로고
    • Pseudo-Anosov homeomorphisms with quadratic expansion
    • to appear
    • J. Franks and E. Rykken, Pseudo-Anosov homeomorphisms with quadratic expansion, (to appear Proc. of the A.M.S.).
    • Proc. of the A.M.S.
    • Franks, J.1    Rykken, E.2
  • 12
    • 0039599626 scopus 로고
    • Growth rate of surface homeomorphisms and flow equivalence
    • D. Fried, Growth rate of surface homeomorphisms and flow equivalence. Erg. Th. & Dyn. Syst. 5(4) (1985), 539-563.
    • (1985) Erg. Th. & Dyn. Syst. , vol.5 , Issue.4 , pp. 539-563
    • Fried, D.1
  • 13
    • 84958434552 scopus 로고
    • Billiards in almost integrable polyhedral surfaces
    • E. Gutkin, Billiards in almost integrable polyhedral surfaces. Erg. Th. & Dyn. Syst. 4 (1984), 569-584.
    • (1984) Erg. Th. & Dyn. Syst. , vol.4 , pp. 569-584
    • Gutkin, E.1
  • 14
    • 0030305240 scopus 로고    scopus 로고
    • The geometry and arithmetic of translation surfaces with applications to polygonal billiards
    • E. Gutkin and C. Judge, The geometry and arithmetic of translation surfaces with applications to polygonal billiards, Math. Res. Lett. 3 (1996), 391-403.
    • (1996) Math. Res. Lett. , vol.3 , pp. 391-403
    • Gutkin, E.1    Judge, C.2
  • 16
    • 0007156637 scopus 로고    scopus 로고
    • Tilings and discrete Dirichlet problems
    • R. Kenyon, Tilings and discrete Dirichlet problems. Isr. J. Math 105 (1998), 61-84.
    • (1998) Isr. J. Math , vol.105 , pp. 61-84
    • Kenyon, R.1
  • 17
    • 0001084159 scopus 로고
    • Problems in low dimensional manifold theory
    • R. Kirby, Problems in low dimensional manifold theory, in Proceed, of Symp. in Pure Math. 32 (1978), 273-312.
    • (1978) Proceed, of Symp. in Pure Math. , vol.32 , pp. 273-312
    • Kirby, R.1
  • 18
    • 84974411733 scopus 로고
    • Propriètés homologiques des feuilletages des surfaces
    • G. Levitt, Propriètés homologiques des feuilletages des surfaces, C.R. Acad. Sci Paris Sér. I Math. 293 (1981), 597-600.
    • (1981) C.R. Acad. Sci Paris Sér. I Math. , vol.293 , pp. 597-600
    • Levitt, G.1
  • 19
    • 0000534712 scopus 로고
    • Hausdorff dimension of sets of nonergodic measured foliations
    • H. Masur, J. Smillie. Hausdorff dimension of sets of nonergodic measured foliations Annals of Math. 134 (1991), 455-543.
    • (1991) Annals of Math. , vol.134 , pp. 455-543
    • Masur, H.1    Smillie, J.2
  • 20
    • 0003279074 scopus 로고
    • Hilbert's third problem: Scissors congruence
    • Pitman (Advanced Publishing Program), Boston, Mass.-London. vi+188 pp.
    • 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.
    • (1979) Research Notes in Mathematics , vol.33
    • Sah, C.H.1
  • 22
    • 0000720459 scopus 로고
    • Asymptotic cycles
    • S. Schwartzman, Asymptotic cycles. Ann. of Math. 66(2) (1957), 270-284.
    • (1957) Ann. of Math. , vol.66 , Issue.2 , pp. 270-284
    • Schwartzman, S.1
  • 25
    • 0001799865 scopus 로고
    • Les surfaces euclidiennes à singulariéts coniques
    • no. 1-2
    • M. Troyanov, Les surfaces euclidiennes à singulariéts coniques. (French) [Euclidean surfaces with conical singularities] Enseign. Math. 32(2) (1986), no. 1-2, 79-94.
    • (1986) Enseign. Math. , vol.32 , Issue.2 , pp. 79-94
    • Troyanov, M.1
  • 26
    • 34249973241 scopus 로고
    • Teichmuller curves in modular space, Eisenstein series, and an application to triangular billiards
    • W. A. Veech, Teichmuller curves in modular space, Eisenstein series, and an application to triangular billiards, Inventiones Math. 97 (1989), 553-583.
    • (1989) Inventiones Math. , vol.97 , pp. 553-583
    • Veech, W.A.1
  • 27
    • 5244300118 scopus 로고
    • The billiard in a regular polygon
    • W. A. Veech, The billiard in a regular polygon, Geom. Func. Anal. 2 (1992), 341-379.
    • (1992) Geom. Func. Anal. , vol.2 , pp. 341-379
    • Veech, W.A.1
  • 28
    • 0039950617 scopus 로고    scopus 로고
    • Plane structures and billiards in rational polyhedra
    • 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.
    • (1996) (Russian) Uspekhi Mat. Nauk , vol.51 , Issue.1 , pp. 145-146
    • Vorobets, Ya.B.1
  • 29
    • 0030517547 scopus 로고    scopus 로고
    • translation
    • 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.
    • (1996) Russian Math. Surveys , vol.51 , Issue.1 , pp. 177-178
  • 30
    • 0039950617 scopus 로고    scopus 로고
    • Plane structures and billiards in rational polygons: The Veech alternative
    • 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.
    • (1996) (Russian) Uspekhi Mat. Nauk , vol.51 , Issue.5 , pp. 3-42
    • Vorobets, Ya.B.1
  • 31
    • 0030344244 scopus 로고    scopus 로고
    • translation
    • 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.
    • (1996) Russian Math. Surveys , vol.51 , Issue.5 , pp. 779-817
  • 33
    • 33645064917 scopus 로고
    • Topological transitivity of billiards in polygons
    • 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.)
    • (1975) Math. Notes of the USSR Acad. Sci. , vol.18 , Issue.2 , pp. 291-300
    • Zemlyakov, A.1    Katok, A.2
  • 34
    • 33645064917 scopus 로고
    • English translation
    • 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.)
    • (1976) Math. Notes , vol.18 , Issue.2 , pp. 760-764


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