Le flot géodésique des variétés riemanniennes à courbure négative

 Access to full text

 Full (PDF)

1. [A1] D.V. Anosov - Roughness of geodesic flows on compact Riemannian manifolds of negative curvature, Dokl. Akad. Nauk. SSSR145 (1962), 707-709, = Soviet Math. Dokl.3 (1962), 1062-1069. Zbl0135.40401MR143156
2. [A2] D.V. Anosov - Geodesic flows on compact manifolds of negative curvature, Trud. Mat. Inst. Steklova90 (1967), = Proc. Steklov Inst., Amer. Math. Soc. Trans. (1969). Zbl0176.19101
3. [Ba1] W. Ballmann - Non positively curved manifolds of higher rank, Ann. Math.112 (1985), 597-609. Zbl0585.53031
4. [BB] W. Ballmann et M. Brin - On the ergodicity of geodesic flows, Ergod. Th. Dynam. Syst.2 (1982), 311-315. Zbl0519.58036MR721726
5. [BBE] W. Ballmann, M. Brin et P. Eberlein - Structure of manifolds of non positive curvature, I, Ann. Math.112 (1985), 171-203. Zbl0589.53047MR799256
6. [BBS] W. Ballmann, M. Brin et R. Spatzier - Structure of manifolds of non positive curvature, II, Ann. Math.112 (1985), 204-235. Zbl0598.53046
7. [BFL] Y. Benoist, P. Foulon, F. Labourie - Flots d'Anosov à distributions stable et instable différentiables, C. R. Acad. Sci. Paris311 (1990), 351-354. Zbl0754.58027MR1071642
8. [Ber] P. Berard - Variétés riemanniennes isospectrales non isométriques, Séminaire Bourbaki, mars 1989, exposé 705, Astérisque177-178 (1989). Zbl0703.53035MR1040571
9. [Bes] A.L. Besse - Manifolds all of whose geodesics are closed, Ergebnisse Band98, Springer, Berlin (1973). Zbl0387.53010MR496885
10. [BCG] G. Besson, G. Courtois, S. Gallot - Volume minimal des espaces localement symétriques, Inventiones Math.103 (1991), 415- 445. Zbl0723.53029MR1085114
11. [Bon] F. Bonahon - Bouts des variétés hyperboliques de dimension trois, Ann. Math.124 (1986), 71-158. Zbl0671.57008MR847953
12. [B] R. Bowen - Periodic orbits for hyperbolic flows, Amer. J. of Math.94 (1972), 1-30. Zbl0254.58005MR298700
13. [BS] K. Burns et R. Spatzier - Manifolds of nonpositive curvature and their buildings, Publ. Math. Inst. Haut. Et. Sci.65 (1987), 35-59. Zbl0643.53037MR908215
14. [C] C. Croke - Rigidity for surfaces of non-positive curvature, Comment. Math. Helvetici65 (1990), 150-169. Zbl0704.53035MR1036134
15. [CF] C. Croke et A. Fathi - An inequality between energy and intersection, Bull. London Math. Soc.22 (1990), 489-494. Zbl0719.53020MR1082022
16. [CFF] C. Croke, A. Fathi et J. Feldman - The marked length spectrum of a surface of negative curvature, à paraître dans Topology. Zbl0779.53025
17. [D] E.I. Dinaburg - A connection between various entropy characterizations of dynamical systems, Izv. Akad. Nauk. SSSR, 35 (1971), 324-366. Zbl0216.44704MR286091
18. [E] P. Eberlein - Geodesic flows on negatively curved manifolds, I, Ann. Math95 (1972), 492-510 ; II, Trans. Amer. Math. Soc.178 (1973), 57-82. Zbl0217.47304MR310926
19. [EH] P. Eberlein et J. Heber - A geometric characterization of symmetric spaces of higher rank, Publ. Math. de l'I.H.E.S.71 (1990), 33-44. Zbl0722.53041MR1079642
20. [EO] P. Eberlein, G. O'Neill - Visibility manifolds, Pacific. J. Math.46 (1973), 45-109. Zbl0264.53026MR336648
21. [FJ] F.T. Farrell et L.E. Jones - Negatively curved manifolds with exotic smooth structures, J. Amer. Math. Soc.2 (1989), 899-908. Zbl0698.53027MR1002632
22. [Gh1] E. Ghys - Flots d'Anosov dont les feuilletages stables sont différentiables, Ann. Sci. Ec. Norm. Sup. Paris20 (1987), 251-270. Zbl0663.58025MR911758
23. [GH2] E. Ghys - L'invariant de Godbillon-Vey, Séminaire Bourbaki, mars 1989, exposé 706, Astérisque177-178 (1989). Zbl0707.57015MR1040572
24. [GH3] E. Ghys - Les groupes hyperboliques, Séminaire Bourbaki, mars 1990, exposé 722, Astérisque (1990). Zbl0744.20036MR1099877
25. [Gr1] M. Gromov - Volume and bounded cohomology, Publ. Math. Inst.Haut.Et.Sci.56 (1982), 5-100. Zbl0516.53046MR686042
26. [Gr2] M. Gromov - Hyperbolic groups, in "Essays in group theory", éd. S.M. Gersten, M.S.R.I. Publ. n° 8, Springer (1987). Zbl0634.20015MR919829
27. [Gr3] M. Gromov - Rigid transformation groups, in "Géométrie différentielle", éd. D. Bernard et Y. Choquet-Bruhat, Travaux en cours33 (1988), 65-139, Hermann, Paris (1988). Zbl0652.53023MR955852
28. [GK] V. Guillemin et D. Kazhdan - Some inverse spectral results for negatively curved 2-manifolds, Topology19 (1980), 301-312. Zbl0465.58027MR579579
29. [H1] J. Hadamard - Les surfaces à courbures opposées et leurs lignes géodésiques, J. Math. Pures Appl.4 (1898), 27-74. JFM29.0522.01
30. [H2] J. Hadamard - Sur l'itération et les solutions asymptotiques des équations différentielles, Bull. Soc. Math. France24 (1901), 224- 228. JFM32.0314.01
31. [Ha1] U. Hamenstädt - A new description of the Bowen-Margulis mea- sure, Ergod. Th. Dynam. Syst.9 (1989), 455-464. Zbl0722.58029MR1016663
32. [Ha2] U. Hamenstädt - Entropy rigidity of locally symmetric spaces of rank one, Ann. Math.131 (1990), 35-52. Zbl0699.53049MR1038357
33. [Has] B. Hasselblatt - Regularity of the Anosov splitting and of horospheric foliations, Prépublication, I.H.E.S. Bures-sur-Yvette (1991). 
34. [He1] G.A. Hedlund - On the metrical transitivity of the geodesics on closed surfaces of constant negative curvatune, Ann. Math.35 (1934), 787-808. Zbl0010.22107MR1503197
35. [He2] G.A. Hedlund - The dynamics of geodesic flows, Bull. Amer. Math. Soc.45 (1939), 241-260. Zbl65.0793.02JFM65.0793.02
36. [HP] M. Hirsch et C. Pugh - Stable manifolds and hyperbolic sets, Proc. Symp. in Pure Math.14 (1970), 133-163. Zbl0215.53001MR271991
37. [Hop] E. Hopf - Statistik der Lösungen geodätischer Probleme vom unstabilen Typus, II, Math. Ann.117 (1940), 590-608. Zbl66.0827.04MR2722JFM66.0827.04
38. [HK] S. Hurder et A. Katok - Differentiability, rigidity and Godbillon-Vey classes, Publ. Inst. Haut. Et. Sci.72 (1990), 5-61. Zbl0725.58034MR1087392
39. [Kan] M. Kanai - Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergod. Th. Dynam. Syst.8 (1988), 215-240. Zbl0634.58020MR951270
40. [Kat] A. Katok - Four applications of conformal equivalence to geometry and dynamics, Erg. Th. Dynam. Syst.8 (1988), 139-152. Zbl0668.58042MR967635
41. [KKK] A. Katok, G. Knieper, M. Pollicott et H. Weiss - Differentiability and entropy for Anosov flows and geodesic flows, Bull. Amer. Math. Soc.22 (1990), 285-293. Zbl0717.58045MR1013257
42. [K] A.N. Kolmogorov - A new metric invariant of transitive systems and automorphisms of Lebesgue spaces, Dohl. Akad. Nauk SSSR119 (1958), 861-864). Zbl0083.10602MR103254
43. [L] A. Livšic - Cohomology of dynamical systems, Isv. Akad. Nauk SSSR36 (1972), 1296-1320, = Math. USSR Izvestia6 (1972), 1278-1301. Zbl0273.58013MR334287
44. [Man] A. Manning - Topological entropy for geodesic flows, Ann. Math.110 (1979), 567-576. Zbl0426.58016MR554385
45. [Mar] G.A. Margulis - On some applications of ergodic theory to the study of manifolds of negative curvature, Funkt. Anal. i Prilozhen.3 (1969), 89-90, = Func. Anal. Appl.3 (1969), 335-336. Zbl0207.20305MR257933
46. [Min] Min Oo - Spectral rigidity for manifolds with negative curvature op- erator, in "Nonlinear Problems in Geometry", Contemporary Math.51 (1986), 99-103. Zbl0591.53041
47. [M1] M. Morse - A one-to-one representation of geodesics, Amer. J. Math.43, (1921), 33-51. Zbl48.0786.05MR1506428JFM48.0786.05
48. [M2] M. Morse - Instability and transitivity, J. Math. Pures Appl.14 (1935), 49-71. Zbl0011.13104
49. [Mos] G.D. Mostow - Strong rigidity of locally symmetric spaces, Ann. of Math. Studies, Vol. 78, Princeton Univ. Press, Princeton (1973). Zbl0265.53039MR385004
50. [O] J.P. Otal - Le spectre marqué des longueurs des surfaces à courburenégative, Ann. Math.131 (1990), 151-162. Zbl0699.58018MR1038361
51. [Pan] P. Pansu - Dimension conforme et sphère à l'infini des variétés à courbure négative, Ann. Acad. Sci. Fennicae14 (1989), 177-212. Zbl0722.53028MR1024425
52. [PP] W. Parry et M. Pollicott - Zeta functions and the periodic orbit structure of hyperbolic dynamics, Astérisque187-188 (1990). Zbl0726.58003MR1085356
53. [Pes] Ya.B. Pesin - Geodesic flows with hyperbolic behaviour of the tra jectories and ob jects connected with them, Uspekhi Math. Nauk36 (1981), 3-31 = Russian Math. Surveys36 (1981), 1-59. Zbl0493.58001MR629682
54. [P] A. Preissmann - Quelques propriétés globales des espaces de Rie- mann, Comm. Math. Helvetici15 (1943), 175-216. Zbl0027.25903MR10459
55. [S] S. Smale - Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967), 747-817. Zbl0202.55202MR228014
56. [Y] J.C. Yoccoz - Polynomes quadratiques et attracteur de Hénon, Séminaire Bourbaki, novembre 1990, exposé 734, Astérisque (1991). Zbl0754.58022MR1157841

1. Étienne Ghys, Dynamique des flots unipotents sur les espaces homogènes