메뉴 건너뛰기




Volumn 133, Issue 4, 2001, Pages 295-339

Cutting sequences for geodesic flow on the modular surface and continued fractions

Author keywords

Continued fractions; Cutting sequences; Modular group; Modular surface; Symbolic dynamics

Indexed keywords


EID: 0039785197     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00010093     Document Type: Article
Times cited : (16)

References (53)
  • 1
    • 0012045291 scopus 로고
    • Geodesic flows, interval maps, and symbolic dynamics
    • Bedford T, Keane M, Series C (eds). Oxford: Univ Press
    • Adler R ( 1991) Geodesic flows, interval maps, and symbolic dynamics. In Bedford T, Keane M, Series C (eds) Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces, pp 93-123. Oxford: Univ Press
    • (1991) Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces , pp. 93-123
    • Adler, R.1
  • 2
    • 23744481957 scopus 로고
    • Cross section maps for geodesic flows I. The modular surface
    • Katok A (ed). Proceedings, Special Year, Maryland 1979-80. Boston: Birkhäuser
    • Adler R, Flatto L (1982) Cross Section Maps for Geodesic Flows I. The Modular Surface. In Katok A (ed) Ergodic Theory and Dynamical Systems II, pp 103-161. Proceedings, Special Year, Maryland 1979-80. Boston: Birkhäuser
    • (1982) Ergodic Theory and Dynamical Systems , vol.2 , pp. 103-161
    • Adler, R.1    Flatto, L.2
  • 3
    • 84967782932 scopus 로고
    • Geodesic flows, interval maps and symbolic dynamics
    • Adler R, Flatto L (1991) Geodesic flows, interval maps and symbolic dynamics. Bull Amer Math Soc 25: 229-334
    • (1991) Bull Amer Math Soc , vol.25 , pp. 229-334
    • Adler, R.1    Flatto, L.2
  • 5
    • 0001888563 scopus 로고
    • Le codage des flot géodésique sur la surface modulaire
    • Arnoux P (1994) Le codage des flot géodésique sur la surface modulaire. Enseign Math 40: 29-48
    • (1994) Enseign Math , vol.40 , pp. 29-48
    • Arnoux, P.1
  • 6
    • 0001497067 scopus 로고
    • Ein mechanisches system mit quasiergodischen Bahnen
    • Collected Papers, pp 499-505
    • Artin E (1924) Ein mechanisches System mit quasiergodischen Bahnen. Hamburger Math Abh 3: 170-175 (Collected Papers, pp 499-505)
    • (1924) Hamburger Math Abh , vol.3 , pp. 170-175
    • Artin, E.1
  • 8
    • 0004223966 scopus 로고
    • Providence, R.I.: Amer Math Soc Revision, J Moser
    • Birkhoff GD (1927) Dynamical Systems. Providence, R.I.: Amer Math Soc (Revision: 1966, J Moser)
    • (1927) Dynamical Systems
    • Birkhoff, G.D.1
  • 9
    • 51249186274 scopus 로고
    • Markov maps associated with Fuchsian groups
    • Bowen R, Series C (1979) Markov maps associated with Fuchsian groups. Publ Math IHES 50: 153-170
    • (1979) Publ Math IHES , vol.50 , pp. 153-170
    • Bowen, R.1    Series, C.2
  • 13
    • 0040070761 scopus 로고
    • Continued fractions and matrices
    • Frame JS (1949) Continued Fractions and Matrices. Amer Math Monthly 56: 98-103
    • (1949) Amer Math Monthly , vol.56 , pp. 98-103
    • Frame, J.S.1
  • 14
    • 38249029518 scopus 로고
    • Hurwitz sequences, the farey process, and generalized continued fractions
    • Goldman JR (1988) Hurwitz sequences, the Farey process, and generalized continued fractions. Adv in Math 72: 239-260
    • (1988) Adv in Math , vol.72 , pp. 239-260
    • Goldman, J.R.1
  • 16
    • 0002998341 scopus 로고
    • Les surfaces á corbures opposseés et leurs lignes geódésiques
    • Ser IV
    • Hadamard J (1898) Les surfaces á corbures opposseés et leurs lignes geódésiques. J de Math 5 (Ser IV): 27-73
    • (1898) J de Math , vol.5 , pp. 27-73
    • Hadamard, J.1
  • 18
    • 0001676788 scopus 로고
    • A metrically transitive group defined by the modular group
    • Hedlund GA (1935) A metrically transitive group defined by the modular group. Amer J Math 52: 668-678
    • (1935) Amer J Math , vol.52 , pp. 668-678
    • Hedlund, G.A.1
  • 19
    • 0001585656 scopus 로고
    • The dynamics of geodesic flows
    • Hedlund GA (1939) The dynamics of geodesic flows. Bull Amer Math Soc 45: 241-260
    • (1939) Bull Amer Math Soc , vol.45 , pp. 241-260
    • Hedlund, G.A.1
  • 20
    • 0002913169 scopus 로고
    • Sur l'introduction des variables continues dans la theorie des nombres
    • Hermite C (1851) Sur l'introduction des variables continues dans la theorie des nombres. J reine Angew Math 41: 191-216
    • (1851) J Reine Angew Math , vol.41 , pp. 191-216
    • Hermite, C.1
  • 22
    • 84902347396 scopus 로고
    • Sur la méthode d'approximation d'Hermite
    • Humbert G (1916) Sur la méthode d'approximation d'Hermite. J Math Pures Appl (7th Ser) 2: 70-103
    • (1916) J Math Pures Appl (7th Ser) , vol.2 , pp. 70-103
    • Humbert, G.1
  • 23
    • 0039300373 scopus 로고
    • Sur les fractiones continues ordinaires et les formes quadatique binaires indéfinies
    • Humbert G (1916) Sur les fractiones continues ordinaires et les formes quadatique binaires indéfinies. J Math Pures Appl (7th Ser) 2: 104-154
    • (1916) J Math Pures Appl (7th Ser) , vol.2 , pp. 104-154
    • Humbert, G.1
  • 24
    • 0040664332 scopus 로고
    • Reduction theory for Fuchsian groups
    • Katok S (1985) Reduction theory for Fuchsian groups. Math Annalen 273: 461-470
    • (1985) Math Annalen , vol.273 , pp. 461-470
    • Katok, S.1
  • 25
    • 0004117363 scopus 로고
    • Chicago: University of Chicago Press
    • Katok S (1992) Fuchsian Groups. Chicago: University of Chicago Press
    • (1992) Fuchsian Groups
    • Katok, S.1
  • 26
    • 0001637921 scopus 로고    scopus 로고
    • Coding of closed geodesics after Gauss and Morse
    • Katok S (1996) Coding of closed geodesics after Gauss and Morse. Geometriae Dedicata 63: 123-145
    • (1996) Geometriae Dedicata , vol.63 , pp. 123-145
    • Katok, S.1
  • 27
    • 0002064981 scopus 로고
    • Riemannsche manningfaltigkeiten und nichteuklidischen raumformen (Vierte mitteilungen: Verlauf geodätischer linien)
    • Köebe P (1929) Riemannsche Manningfaltigkeiten und nichteuklidischen Raumformen (Vierte Mitteilungen: Verlauf Geodätischer Linien). Sitzb Preuss Akad Wiss 1929: 414-457
    • (1929) Sitzb Preuss Akad Wiss , vol.1929 , pp. 414-457
    • Köebe, P.1
  • 28
    • 0038886314 scopus 로고
    • Continued fractions and linear substitutions
    • Kolden K (1949) Continued fractions and linear substitutions. Arch Math og Naturvid 50: 141-196
    • (1949) Arch Math Og Naturvid , vol.50 , pp. 141-196
    • Kolden, K.1
  • 29
    • 0001931441 scopus 로고
    • Number theory and dynamical systems
    • Burr SA (ed) The Unreasonable Effectiveness of Number Theory. Providence, R.I.: Amer Math Soc
    • Lagarias JC (1992) Number theory and dynamical systems. In Burr SA (ed) The Unreasonable Effectiveness of Number Theory, pp 35-72. Proc Symp Appl Math 46. Providence, R.I.: Amer Math Soc
    • (1992) Proc Symp Appl Math , vol.46 , pp. 35-72
    • Lagarias, J.C.1
  • 30
    • 84963045409 scopus 로고
    • Geodesic multidimensional continued fractions
    • Lagarias JC (1994) Geodesic multidimensional continued fractions. Proc London Math Soc 69: 464-488
    • (1994) Proc London Math Soc , vol.69 , pp. 464-488
    • Lagarias, J.C.1
  • 31
    • 84976041172 scopus 로고
    • The continuous diophantine approximation mapping of Szekeres
    • Lagarias JC, Pollington AM (1995) The continuous Diophantine approximation mapping of Szekeres. J Australian Math Soc, Ser A 59: 148-172
    • (1995) J Australian Math Soc, Ser A , vol.59 , pp. 148-172
    • Lagarias, J.C.1    Pollington, A.M.2
  • 32
    • 0029301829 scopus 로고
    • A walk along the branches of the extended farey tree
    • Lagarias JC, Tresser CP (1995) A walk along the branches of the extended Farey tree, IBM J Res Dev 39: 283-294
    • (1995) IBM J Res Dev , vol.39 , pp. 283-294
    • Lagarias, J.C.1    Tresser, C.P.2
  • 35
    • 0000500765 scopus 로고
    • On poincaré's theorem for fundamental polygons
    • Maskit B (1971) On Poincaré's theorem for fundamental polygons. Adv in Math 7: 219-230
    • (1971) Adv in Math , vol.7 , pp. 219-230
    • Maskit, B.1
  • 36
    • 0039284500 scopus 로고
    • Geodesics on modular surfaces and continued fractions
    • Moeckel R (1982) Geodesics on modular surfaces and continued fractions. Ergod Th Dynam Sys 2: 69-83
    • (1982) Ergod Th Dynam Sys , vol.2 , pp. 69-83
    • Moeckel, R.1
  • 37
    • 0002815390 scopus 로고
    • A one-to-one representation of geodesics on a surface of negative curvature
    • Morse M (1921) A one-to-one representation of geodesics on a surface of negative curvature. Amer J Math 43: 33-51
    • (1921) Amer J Math , vol.43 , pp. 33-51
    • Morse, M.1
  • 38
    • 84914087454 scopus 로고
    • Recurrent geodesics on a surface of negative curvature
    • Morse M (1921) Recurrent geodesics on a surface of negative curvature. Trans Amer Math Soc 22: 84-100
    • (1921) Trans Amer Math Soc , vol.22 , pp. 84-100
    • Morse, M.1
  • 41
    • 0001511585 scopus 로고
    • Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen
    • Nielsen J (1927) Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen. Acta Math 50: 189-358
    • (1927) Acta Math , vol.50 , pp. 189-358
    • Nielsen, J.1
  • 42
    • 0038236755 scopus 로고
    • Diophantine approximation via the modular group
    • Nicholls PJ (1978) Diophantine approximation via the modular group. J London Math Soc 17: 11-17
    • (1978) J London Math Soc , vol.17 , pp. 11-17
    • Nicholls, P.J.1
  • 43
    • 0001581551 scopus 로고
    • On continued fractions and finite automata
    • Raney GN (1973) On continued fractions and finite automata. Math Annalen 206: 265-283
    • (1973) Math Annalen , vol.206 , pp. 265-283
    • Raney, G.N.1
  • 44
    • 0040070758 scopus 로고
    • Continued fractions without tears
    • Richards I (1981) Continued fractions without tears. Math Mag 54: 163-171
    • (1981) Math Mag , vol.54 , pp. 163-171
    • Richards, I.1
  • 45
    • 0001196157 scopus 로고
    • Symbolic dynamics for geodesic flows
    • Series C (1981) Symbolic dynamics for geodesic flows. Acta Math 146: 103-128
    • (1981) Acta Math , vol.146 , pp. 103-128
    • Series, C.1
  • 46
    • 0002189261 scopus 로고
    • The modular surface and continued fractions
    • Correction: see [49, p. 148]
    • Series C (1985) The modular surface and continued fractions. J London Math Soc 31: 69-80 (Correction: see [49, p. 148])
    • (1985) J London Math Soc , vol.31 , pp. 69-80
    • Series, C.1
  • 47
    • 0002769875 scopus 로고
    • The geometry of Markoff numbers
    • Series C (1985) The geometry of Markoff numbers. Math Intelligencer 7(3): 20-29
    • (1985) Math Intelligencer , vol.7 , Issue.3 , pp. 20-29
    • Series, C.1
  • 48
    • 84974137974 scopus 로고
    • Geometric Markov coding on surfaces of constant negative curvature
    • Series C (1986) Geometric Markov coding on surfaces of constant negative curvature. Ergod Th Dynam Sys 6: 601-625
    • (1986) Ergod Th Dynam Sys , vol.6 , pp. 601-625
    • Series, C.1
  • 49
    • 0001836601 scopus 로고
    • Geometrical methods of symbolic coding
    • Bedford T, Keane M, Series C (eds). Oxford: Univ Press
    • Series C (1991) Geometrical methods of symbolic coding. In Bedford T, Keane M, Series C (eds) Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, pp 125-151. Oxford: Univ Press
    • (1991) Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces , pp. 125-151
    • Series, C.1
  • 50
    • 0040664330 scopus 로고
    • Memoire sur les equations modulaires. Atti Accad dei Lincei
    • 1877
    • Smith HJS (1877) Memoire sur les equations modulaires. Atti Accad dei Lincei, Memorie Sci Phys Mat Nat Ser III, Vol I 1877, 136-149. In Collected Mathematical Papers, Volume II, pp 224-241. New York: Chelsea, 1965
    • (1877) Memorie Sci Phys Mat Nat Ser III , vol.1 , pp. 136-149
    • Smith, H.J.S.1
  • 51
    • 0039479047 scopus 로고
    • New York: Chelsea
    • Smith HJS (1877) Memoire sur les equations modulaires. Atti Accad dei Lincei, Memorie Sci Phys Mat Nat Ser III, Vol I 1877, 136-149. In Collected Mathematical Papers, Volume II, pp 224-241. New York: Chelsea, 1965
    • (1965) Collected Mathematical Papers , vol.2 , pp. 224-241


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.