메뉴 건너뛰기




Volumn 1, Issue PART A, 2002, Pages 453-545

Chapter 6 Hyperbolic dynamics and riemannian geometry

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0042080490     PISSN: 1874575X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1874-575X(02)80008-X     Document Type: Article
Times cited : (93)

References (83)
  • 1
    • 33751347915 scopus 로고    scopus 로고
    • Hyperbolic dynamical systems
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Hasselblatt B. Hyperbolic dynamical systems. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 239-319
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 239-319
    • Hasselblatt, B.1
  • 2
    • 9344247607 scopus 로고    scopus 로고
    • Principle structures
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Katok A., and Hasselblatt B. Principle structures. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 1-203
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 1-203
    • Katok, A.1    Hasselblatt, B.2
  • 3
    • 67649354433 scopus 로고    scopus 로고
    • Periodic orbits and zeta functions
    • Hasselblatt B., and Katok A. (Eds), Elsevier, Amsterdam
    • Pollicott M. Periodic orbits and zeta functions. In: Hasselblatt B., and Katok A. (Eds). Handbook of Dynamical Systems Vol. 1A (2002), Elsevier, Amsterdam 409-453
    • (2002) Handbook of Dynamical Systems , vol.1 A , pp. 409-453
    • Pollicott, M.1
  • 4
    • 0002564801 scopus 로고
    • Geodesic flows on closed Riemannian manifolds with negative curvature
    • Anosov D.V. Geodesic flows on closed Riemannian manifolds with negative curvature. Proc. Steklov. Inst. Math. 90 (1967)
    • (1967) Proc. Steklov. Inst. Math. , vol.90
    • Anosov, D.V.1
  • 5
    • 0001123306 scopus 로고
    • Nonpositively curved manifolds of higher rank
    • Ballmann W. Nonpositively curved manifolds of higher rank. Annals of Math. 122 (1985) 597-609
    • (1985) Annals of Math. , vol.122 , pp. 597-609
    • Ballmann, W.1
  • 6
    • 0003223423 scopus 로고
    • Lectures on Spaces of Nonpositive Curvature
    • Ballmann W. Lectures on Spaces of Nonpositive Curvature. DMV Seminar Band 25 (1995)
    • (1995) DMV Seminar , vol.Band 25
    • Ballmann, W.1
  • 7
    • 0000632933 scopus 로고
    • Structure of manifolds of nonpositive curvature
    • Ballmann W., Brin M., and Eberlein P. Structure of manifolds of nonpositive curvature. Annals of Math. 122 (1985) 171-203
    • (1985) Annals of Math. , vol.122 , pp. 171-203
    • Ballmann, W.1    Brin, M.2    Eberlein, P.3
  • 8
    • 0003331011 scopus 로고
    • Manifolds of Nonpositive Curvature
    • Birkhäuser, Boston
    • Ballmann W., Gromov M., and Schroeder V. Manifolds of Nonpositive Curvature. Progress in Math. Vol. 61 (1985), Birkhäuser, Boston
    • (1985) Progress in Math. , vol.61
    • Ballmann, W.1    Gromov, M.2    Schroeder, V.3
  • 9
    • 0002068964 scopus 로고
    • Flots d'Anosov à distributions stable et instable dijférentiables
    • Benoist Y., Foulon P., and Labourie F. Flots d'Anosov à distributions stable et instable dijférentiables. J. Amer. Math. Soc. 5 (1992) 33-74
    • (1992) J. Amer. Math. Soc. , vol.5 , pp. 33-74
    • Benoist, Y.1    Foulon, P.2    Labourie, F.3
  • 10
    • 0000168310 scopus 로고
    • Entropies et rigidités des espaces localement symétriques de courbure strictement négative
    • Besson G., Courtois G., and Gallot S. Entropies et rigidités des espaces localement symétriques de courbure strictement négative. GAFA 5 (1995) 731-799
    • (1995) GAFA , vol.5 , pp. 731-799
    • Besson, G.1    Courtois, G.2    Gallot, S.3
  • 12
    • 0011912447 scopus 로고
    • Entropy-expansive maps
    • Bowen R. Entropy-expansive maps. Trans. Amer. Math. Soc. 164 (1972) 321-331
    • (1972) Trans. Amer. Math. Soc. , vol.164 , pp. 321-331
    • Bowen, R.1
  • 13
    • 0002729084 scopus 로고
    • Periodic orbits for hyperbolic flows
    • Bowen R. Periodic orbits for hyperbolic flows. Amer. J. Math. 94 (1972) 1-30
    • (1972) Amer. J. Math. , vol.94 , pp. 1-30
    • Bowen, R.1
  • 14
    • 0040011089 scopus 로고
    • Maximizing entropy for a hyperbolic flow
    • Bowen R. Maximizing entropy for a hyperbolic flow. Math. Systems Theory 7 (1973) 300-303
    • (1973) Math. Systems Theory , vol.7 , pp. 300-303
    • Bowen, R.1
  • 15
    • 0001902704 scopus 로고
    • Unique ergodicity for horocycle foliations
    • Bowen R., and Marcus B. Unique ergodicity for horocycle foliations. Israel J. Math. 36 (1977) 43-67
    • (1977) Israel J. Math. , vol.36 , pp. 43-67
    • Bowen, R.1    Marcus, B.2
  • 16
    • 0003195612 scopus 로고    scopus 로고
    • Metric Spaces of Non-Positive Curvature
    • Springer
    • Bridson M.R., and Haefliger A. Metric Spaces of Non-Positive Curvature. Grund. Math. Wissensch. Vol. 319 (1999), Springer
    • (1999) Grund. Math. Wissensch. , vol.319
    • Bridson, M.R.1    Haefliger, A.2
  • 17
    • 67649370283 scopus 로고    scopus 로고
    • Private communication
    • K. Burns, Private communication.
    • Burns, K.1
  • 19
    • 51249174959 scopus 로고
    • Manifolds of nonpositive curvature and their buildings
    • Burns K., and Spatzier R. Manifolds of nonpositive curvature and their buildings. IHES 65 (1987) 35-59
    • (1987) IHES , vol.65 , pp. 35-59
    • Burns, K.1    Spatzier, R.2
  • 20
    • 84963057263 scopus 로고
    • Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2
    • Burger M. Intersection, the Manhattan curve, and Patterson-Sullivan theory in rank 2. Int. Math. Res. Notices 7 (1993) 217-225
    • (1993) Int. Math. Res. Notices , vol.7 , pp. 217-225
    • Burger, M.1
  • 22
    • 51249163743 scopus 로고
    • Regularity of topological and metric entropy of hyperbolic flows
    • Contreras G. Regularity of topological and metric entropy of hyperbolic flows. Math. Z. 201 (1992) 97-112
    • (1992) Math. Z. , vol.201 , pp. 97-112
    • Contreras, G.1
  • 23
    • 51249175631 scopus 로고
    • Rigidity for surfaces of non-positive curvature
    • Croke C.B. Rigidity for surfaces of non-positive curvature. Comment. Math. Helv. 65 (1990) 150-169
    • (1990) Comment. Math. Helv. , vol.65 , pp. 150-169
    • Croke, C.B.1
  • 24
    • 0000728873 scopus 로고
    • The marked length-spectrum of a surface of nonpositive curvature
    • Croke C.B., Fathi A., and Feldman J. The marked length-spectrum of a surface of nonpositive curvature. Topology 31 4 (1992) 847-855
    • (1992) Topology , vol.31 , Issue.4 , pp. 847-855
    • Croke, C.B.1    Fathi, A.2    Feldman, J.3
  • 25
    • 67649355668 scopus 로고    scopus 로고
    • Spectral rigidity of a compact negatively curved manifold
    • Preprint
    • C. Croke and V. Sharafutdinov, Spectral rigidity of a compact negatively curved manifold, Preprint.
    • Croke, C.1    Sharafutdinov, V.2
  • 26
  • 27
    • 67649301807 scopus 로고    scopus 로고
    • P. Eberlein, Geometry of Nonpositively Curved Manifolds, Chicago Lecture Notes in Math
    • P. Eberlein, Geometry of Nonpositively Curved Manifolds, Chicago Lecture Notes in Math.
  • 29
    • 84968484221 scopus 로고
    • Negatively curved manifolds with exotic smooth structures
    • Farrell F., and Jones L. Negatively curved manifolds with exotic smooth structures. J. Amer. Math. Soc. 2 (1989) 899-908
    • (1989) J. Amer. Math. Soc. , vol.2 , pp. 899-908
    • Farrell, F.1    Jones, L.2
  • 30
    • 84968487211 scopus 로고
    • A topological analogue of Mostov's rigidity theorem
    • Farrell F., and Jones L. A topological analogue of Mostov's rigidity theorem. J. Amer. Math. Soc. 2 (1989) 257-370
    • (1989) J. Amer. Math. Soc. , vol.2 , pp. 257-370
    • Farrell, F.1    Jones, L.2
  • 31
    • 67649325694 scopus 로고    scopus 로고
    • Private communication
    • A. Fathi, Private communication.
    • Fathi, A.1
  • 32
    • 0002304365 scopus 로고
    • Travaux de Thurston sur les surfaces
    • Soc. Math. France, Paris
    • Fathi A., Laudenbach F., and Poénaru V. Travaux de Thurston sur les surfaces. Astérisque Vol. 66/67 (1979), Soc. Math. France, Paris
    • (1979) Astérisque , vol.66-67
    • Fathi, A.1    Laudenbach, F.2    Poénaru, V.3
  • 33
    • 84971945662 scopus 로고
    • Geodesic flows on manifolds of negative curvature with smooth horospheric foliations
    • Feres R. Geodesic flows on manifolds of negative curvature with smooth horospheric foliations. Ergodic Theory Dynamical Systems 11 (1991) 653-686
    • (1991) Ergodic Theory Dynamical Systems , vol.11 , pp. 653-686
    • Feres, R.1
  • 34
    • 84974433613 scopus 로고
    • Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows
    • Feres R., and Katok A. Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows. Ergodic Theory Dynamical Systems 8 (1989) 427-4432
    • (1989) Ergodic Theory Dynamical Systems , vol.8 , pp. 427-4432
    • Feres, R.1    Katok, A.2
  • 35
    • 0010534475 scopus 로고
    • Sur les variétés compactes asymptotiquement harmoniques
    • Foulon P., and Labourie F. Sur les variétés compactes asymptotiquement harmoniques. Invent. Math. 109 (1992) 97-111
    • (1992) Invent. Math. , vol.109 , pp. 97-111
    • Foulon, P.1    Labourie, F.2
  • 36
    • 0001406958 scopus 로고
    • On the entropy of the geodesic flow in manifolds without conjugate points
    • Freire A., and Mañé R. On the entropy of the geodesic flow in manifolds without conjugate points. Invent. Math. 69 (1982) 375-392
    • (1982) Invent. Math. , vol.69 , pp. 375-392
    • Freire, A.1    Mañé, R.2
  • 37
    • 0001654823 scopus 로고
    • Flots d'Anosov dont les feuilletages stables sont différentiables
    • Ghys E. Flots d'Anosov dont les feuilletages stables sont différentiables. Ann. Sci. École Norm. Sup. 20 (1987) 251-270
    • (1987) Ann. Sci. École Norm. Sup. , vol.20 , pp. 251-270
    • Ghys, E.1
  • 38
    • 84972567571 scopus 로고
    • The generalized geodesic flow
    • Green L. The generalized geodesic flow. Duke Math. J. 41 (1974) 115-126
    • (1974) Duke Math. J. , vol.41 , pp. 115-126
    • Green, L.1
  • 39
    • 0003273754 scopus 로고
    • Riemannsche Geometrie im Großen
    • Springer-Verlag, Heidelberg
    • Gromoll D., Klingenberg W., and Meyer W. Riemannsche Geometrie im Großen. Lecture Notes in Math. Vol. 55 (1968), Springer-Verlag, Heidelberg
    • (1968) Lecture Notes in Math. , vol.55
    • Gromoll, D.1    Klingenberg, W.2    Meyer, W.3
  • 40
    • 0013172827 scopus 로고    scopus 로고
    • Three remarks on geodesic dynamics and fundamental group
    • Preprint
    • M. Gromov, Three remarks on geodesic dynamics and fundamental group, Preprint.
    • Gromov, M.1
  • 41
    • 84956267209 scopus 로고
    • Filling Riemannian manifolds
    • Gromov M. Filling Riemannian manifolds. J. Differential Geom. 18 (1983) 1-147
    • (1983) J. Differential Geom. , vol.18 , pp. 1-147
    • Gromov, M.1
  • 42
    • 0003195390 scopus 로고
    • Hyperbolic groups. Essays in Group Theory
    • Gromov M. Hyperbolic groups. Essays in Group Theory. Math. Sci. Res. Inst. Publ. Springer Vol. 8 (1987) 75-263
    • (1987) Math. Sci. Res. Inst. Publ. Springer , vol.8 , pp. 75-263
    • Gromov, M.1
  • 43
    • 0002065433 scopus 로고
    • Rigid transformation groups
    • Bernard D., and Choquet-Bruhat Y. (Eds), Hermann
    • Gromov M. Rigid transformation groups. In: Bernard D., and Choquet-Bruhat Y. (Eds). Géométrie Différentielle, Travaux en Cours Vol. 33 (1988), Hermann 65-139
    • (1988) Géométrie Différentielle, Travaux en Cours , vol.33 , pp. 65-139
    • Gromov, M.1
  • 44
    • 0000125310 scopus 로고
    • Some inverse spectral results for negatively curved n-manifolds
    • Guillemin V., and Kazhdan D. Some inverse spectral results for negatively curved n-manifolds. Proc. of Symposia of Pure Math. Vol. 36 (1980) 153-180
    • (1980) Proc. of Symposia of Pure Math. , vol.36 , pp. 153-180
    • Guillemin, V.1    Kazhdan, D.2
  • 45
    • 0001232465 scopus 로고
    • Some inverse spectral results for negatively curved 2-manifolds
    • Guillemin V., and Kazhdan D. Some inverse spectral results for negatively curved 2-manifolds. Topology 19 (1980) 301-312
    • (1980) Topology , vol.19 , pp. 301-312
    • Guillemin, V.1    Kazhdan, D.2
  • 46
    • 0040871485 scopus 로고
    • Time preserving conjugacies of geodesic flows
    • Hamenstädt U. Time preserving conjugacies of geodesic flows. Ergodic Theory Dynamical Systems 12 (1992) 67-74
    • (1992) Ergodic Theory Dynamical Systems , vol.12 , pp. 67-74
    • Hamenstädt, U.1
  • 47
    • 0010966953 scopus 로고
    • Invariant two-forms for geodesic flows
    • Hamenstädt U. Invariant two-forms for geodesic flows. Math. Ann. 301 (1995) 677-698
    • (1995) Math. Ann. , vol.301 , pp. 677-698
    • Hamenstädt, U.1
  • 49
    • 84972541932 scopus 로고
    • Smoothness of horocycle foliations
    • Hirsch M., and Pugh C. Smoothness of horocycle foliations. J. Differential Geom. 10 (1975) 225-238
    • (1975) J. Differential Geom. , vol.10 , pp. 225-238
    • Hirsch, M.1    Pugh, C.2
  • 51
    • 0000683114 scopus 로고
    • Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung
    • Hopf E. Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Ber. Verh. Sachs. Akad. Wiss. Leipzig Vol. 91 (1939) 261-304
    • (1939) Ber. Verh. Sachs. Akad. Wiss. Leipzig , vol.91 , pp. 261-304
    • Hopf, E.1
  • 52
    • 51249176245 scopus 로고
    • Differentiability, rigidity and Godbillon-Vey classes for Anosov flows
    • Hurder S., and Katok A. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Publ. Math. IHES 72 (1990) 5-61
    • (1990) Publ. Math. IHES , vol.72 , pp. 5-61
    • Hurder, S.1    Katok, A.2
  • 54
    • 0037788364 scopus 로고    scopus 로고
    • Nonpositive Curvature: Geometric and Analytics Aspects
    • Birkhäuser, ETH Zürich
    • Jost J. Nonpositive Curvature: Geometric and Analytics Aspects. Lectures in Mathematics (1997), Birkhäuser, ETH Zürich
    • (1997) Lectures in Mathematics
    • Jost, J.1
  • 55
    • 84974277573 scopus 로고
    • Geodesic flows on negatively curved manifolds with smooth stable and unstable foliations
    • Kanai M. Geodesic flows on negatively curved manifolds with smooth stable and unstable foliations. Ergodic Theory Dynamical Systems 8 (1988) 215-239
    • (1988) Ergodic Theory Dynamical Systems , vol.8 , pp. 215-239
    • Kanai, M.1
  • 58
    • 0001882824 scopus 로고
    • Differentiability and analyticity of topological entropy for Anosov and geodesic flows
    • Katok A., Knieper G., Pollicott M., and Weiss H. Differentiability and analyticity of topological entropy for Anosov and geodesic flows. Invent. Math. 98 (1989) 581-597
    • (1989) Invent. Math. , vol.98 , pp. 581-597
    • Katok, A.1    Knieper, G.2    Pollicott, M.3    Weiss, H.4
  • 59
    • 0001812718 scopus 로고
    • Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows
    • Katok A., Knieper G., and Weiss H. Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows. Comm. Math. Phys. 138 (1991) 19-31
    • (1991) Comm. Math. Phys. , vol.138 , pp. 19-31
    • Katok, A.1    Knieper, G.2    Weiss, H.3
  • 60
    • 0013520635 scopus 로고
    • Riemannian manifolds with geodesic flow of Anosov type
    • Klingenberg W. Riemannian manifolds with geodesic flow of Anosov type. Ann. of Math. 99 (1974) 1-13
    • (1974) Ann. of Math. , vol.99 , pp. 1-13
    • Klingenberg, W.1
  • 62
    • 0001064108 scopus 로고
    • Das Wachstum der Äquivalenzklassen geschlossener Geodätischer in kompakten Riemannschen Mannigfaltigkeiten
    • Knieper G. Das Wachstum der Äquivalenzklassen geschlossener Geodätischer in kompakten Riemannschen Mannigfaltigkeiten. Arch. Math. 40 (1983) 559-568
    • (1983) Arch. Math. , vol.40 , pp. 559-568
    • Knieper, G.1
  • 63
    • 0010716481 scopus 로고
    • Spherical means on compact Riemannian manifolds of negative curvature
    • Knieper G. Spherical means on compact Riemannian manifolds of negative curvature. Differential Geom. Appl. 4 (1994) 361-390
    • (1994) Differential Geom. Appl. , vol.4 , pp. 361-390
    • Knieper, G.1
  • 64
    • 0002354343 scopus 로고
    • Volume growth, entropy and the geodesic stretch
    • Knieper G. Volume growth, entropy and the geodesic stretch. Math. Res. Lett. 2 (1995) 1-20
    • (1995) Math. Res. Lett. , vol.2 , pp. 1-20
    • Knieper, G.1
  • 65
    • 0031285548 scopus 로고    scopus 로고
    • On the asymptotic geometry of nonpositively curved manifolds
    • Knieper G. On the asymptotic geometry of nonpositively curved manifolds. GAFA 7 (1997) 755-782
    • (1997) GAFA , vol.7 , pp. 755-782
    • Knieper, G.1
  • 66
    • 0032327527 scopus 로고    scopus 로고
    • The uniqueness of the measure of maximal entropy for geodesic flows on rank I manifolds
    • Knieper G. The uniqueness of the measure of maximal entropy for geodesic flows on rank I manifolds. Ann. of Math. 148 (1998) 291-314
    • (1998) Ann. of Math. , vol.148 , pp. 291-314
    • Knieper, G.1
  • 67
    • 51249174128 scopus 로고
    • Harmonic measure and Bowen-Margulis measures
    • Ledrappier F. Harmonic measure and Bowen-Margulis measures. Israel J. Math. 71 (1990) 275-287
    • (1990) Israel J. Math. , vol.71 , pp. 275-287
    • Ledrappier, F.1
  • 68
    • 0000694245 scopus 로고
    • Some homological properties of U-systems
    • Livšic A.N. Some homological properties of U-systems. Mat. Zametki 10 (1971) 555-564
    • (1971) Mat. Zametki , vol.10 , pp. 555-564
    • Livšic, A.N.1
  • 69
    • 0000174457 scopus 로고
    • Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation
    • de la Llave R. Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation. Ann. of Math. 123 (1986) 537-611
    • (1986) Ann. of Math. , vol.123 , pp. 537-611
    • de la Llave, R.1
  • 70
    • 0000719919 scopus 로고
    • On a theorem of Klingenberg, Dynamical Systems and Bifurcation Theory
    • Camacho M., Pacifico M., and Takens F. (Eds)
    • Mañé R. On a theorem of Klingenberg, Dynamical Systems and Bifurcation Theory. In: Camacho M., Pacifico M., and Takens F. (Eds). Pitman Research Notes in Math. Vol. 160 (1987) 319-345
    • (1987) Pitman Research Notes in Math. , vol.160 , pp. 319-345
    • Mañé, R.1
  • 71
    • 0001472050 scopus 로고
    • Topological entropy for geodesic flows
    • Manning A. Topological entropy for geodesic flows. Ann. of Math. 110 (1979) 567-573
    • (1979) Ann. of Math. , vol.110 , pp. 567-573
    • Manning, A.1
  • 72
    • 0002061809 scopus 로고
    • Certain measures associated with U-flows on compact manifolds
    • Margulis G.A. Certain measures associated with U-flows on compact manifolds. Funct. Anal. Appl. 4 (1970) 55-67
    • (1970) Funct. Anal. Appl. , vol.4 , pp. 55-67
    • Margulis, G.A.1
  • 73
    • 33646837301 scopus 로고
    • Spectral rigidity for manifolds with negative curvature operator
    • Min-Oo M. Spectral rigidity for manifolds with negative curvature operator. Contemp. Math. 51 (1986) 99-103
    • (1986) Contemp. Math. , vol.51 , pp. 99-103
    • Min-Oo, M.1
  • 74
    • 0001788461 scopus 로고
    • A fundamental class of geodesics on any closed surface of genus greater than one
    • Morse M. A fundamental class of geodesics on any closed surface of genus greater than one. Trans. Amer. Math. Soc. 26 (1924) 25-60
    • (1924) Trans. Amer. Math. Soc. , vol.26 , pp. 25-60
    • Morse, M.1
  • 75
    • 0000567068 scopus 로고
    • Le spectre marqué des surfaces à courbure négative
    • Otal J.-P. Le spectre marqué des surfaces à courbure négative. Ann. of Math. (2) 131 (1990) 151-162
    • (1990) Ann. of Math. (2) , vol.131 , pp. 151-162
    • Otal, J.-P.1
  • 77
    • 0000131067 scopus 로고
    • The limit set of Fuchsian group
    • Patterson S. The limit set of Fuchsian group. Acta Math. 136 (1976) 241-273
    • (1976) Acta Math. , vol.136 , pp. 241-273
    • Patterson, S.1
  • 78
    • 84961291543 scopus 로고
    • Characteristic Lyapunov exponents and smooth ergodic theory
    • Pesin Ya. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surv. 32 (1977) 54-114
    • (1977) Russian Math. Surv. , vol.32 , pp. 54-114
    • Pesin, Ya.1
  • 79
    • 51249179988 scopus 로고
    • An inequality for the entropy of differentiable maps
    • Ruelle D. An inequality for the entropy of differentiable maps. Bol. Soc. Bras. Mat. 9 (1978) 83-87
    • (1978) Bol. Soc. Bras. Mat. , vol.9 , pp. 83-87
    • Ruelle, D.1
  • 82
    • 51249182653 scopus 로고
    • The density at infinity of a discrete group of hyperbolic motions
    • Sullivan D. The density at infinity of a discrete group of hyperbolic motions. Inst. Hautes Études Sci. Publ. Math. 50 (1979) 171-202
    • (1979) Inst. Hautes Études Sci. Publ. Math. , vol.50 , pp. 171-202
    • Sullivan, D.1
  • 83
    • 0003904893 scopus 로고
    • An Introduction to Ergodic Theory
    • Springer-Verlag, Berlin
    • Walters P. An Introduction to Ergodic Theory. Graduate Texts in Mathematics (1982), Springer-Verlag, Berlin
    • (1982) Graduate Texts in Mathematics
    • Walters, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.